What motives lead to Faust's wager with Mephistopheles, and what are the terms of that wager in Goethe's Faust Part I?

This is a complex portion of Goethe's poem. Understanding
Faust's motive is dependent upon (1) understanding his quest and unrest as revealed in
"Night" and "Before the City-Gate"; (2) understanding the wager between The Lord and
Mephistopheles in "Prologue in Heaven”; (3) and understanding the importance of the
theme of change Goethe's Faust. This theme is introduced in the
Prologue when The Lord says to Mephistopheles,

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Sees not the gardener, even while buds his
tree,
Both flower and fruit the future years
adorning?

This establishes
the idea that within one state of being, another state of being--the next state of
being--lies waiting. In other words, change lies waiting as the natural progression of
being. The wager The Lord strikes with Mephistopheles is based on this idea. The Lord
replies to Mephistopheles' suggestion of a bet ("What will you bet?") by saying that a
good person will always be led by "an instinct of the one true way." In relation to
change as the natural progression of being, The Lord's reply means that within Faust
lies the blossoms and the fruit that follow the buds: "Both flower and fruit the future
years adorning."

Faust's yearning, as he expresses it to
Wagner in "Before the City-Gate," is to have a unity between what one knows and what one
uses and to have a unity between the two parts of his
soul:

That
which one does not know, one needs to use;
And what one knows, one uses never.
/... /
Two souls, alas! reside within my breast,
And each withdraws
from, and repels, its
brother.

Faust feels great
unrest within himself; it is this unrest that compels him in "Night." It is this unrest
that leads him--that motivates him--to set the terms of a wager with Mephistopheles. His
quest is to find that thing that known is needed and that needed is known--that one
thing that unifies. This is why he turns to magic and the cosmos--he expects to find in
it the power that unifies and unites:

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O happy he, who still renews
The hope,
from Error's deeps to rise
forever!

The terms of the
wager Faust makes with Mephistopheles reflect this yearning and quest. He says, in
essence, if ever Mephistopheles makes his divided nature quiet; if flattery can make him
view himself with pleasure (replacing yearning); if enjoyments can turn his mind from
his quest; when Faust calls for time to stop, then Mephistopheles can claim Faust. In
other words, the wager may be paraphrased as, "Soothe my yearning and satisfy my quest
and make me desire to live, then you win my soul." Note how this reflects the wager The
Lord made with Mephistopheles: the flower and fruit are bound together, and a good
person “Has still an instinct of the one true way.” Faust's wager
is:

When on
an idler's bed I stretch myself in quiet, ...
Until, self-pleased, myself I
see,—
Canst thou with rich enjoyment fool me,
Let that day be the
last for me!
The bet I offer. / ... /
When thus I hail the Moment
flying:
"Ah, still delay—thou art so fair!"
Then bind me in thy
bonds undying, ....