(v-3)(v-3)=2v^2-7v+7

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Solution for (v-3)(v-3)=2v^2-7v+7 equation: 


Simplifying
(v + -3)(v + -3) = 2v2 + -7v + 7

Reorder the terms:
(-3 + v)(v + -3) = 2v2 + -7v + 7

Reorder the terms:
(-3 + v)(-3 + v) = 2v2 + -7v + 7

Multiply (-3 + v) * (-3 + v)
(-3(-3 + v) + v(-3 + v)) = 2v2 + -7v + 7
((-3 * -3 + v * -3) + v(-3 + v)) = 2v2 + -7v + 7
((9 + -3v) + v(-3 + v)) = 2v2 + -7v + 7
(9 + -3v + (-3 * v + v * v)) = 2v2 + -7v + 7
(9 + -3v + (-3v + v2)) = 2v2 + -7v + 7

Combine like terms: -3v + -3v = -6v
(9 + -6v + v2) = 2v2 + -7v + 7

Reorder the terms:
9 + -6v + v2 = 7 + -7v + 2v2

Solving
9 + -6v + v2 = 7 + -7v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + -7 + -6v + 7v + v2 + -2v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Combine like terms: 9 + -7 = 2
2 + -6v + 7v + v2 + -2v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Combine like terms: -6v + 7v = 1v
2 + 1v + v2 + -2v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Combine like terms: v2 + -2v2 = -1v2
2 + 1v + -1v2 = 7 + -7v + 2v2 + -7 + 7v + -2v2

Reorder the terms:
2 + 1v + -1v2 = 7 + -7 + -7v + 7v + 2v2 + -2v2

Combine like terms: 7 + -7 = 0
2 + 1v + -1v2 = 0 + -7v + 7v + 2v2 + -2v2
2 + 1v + -1v2 = -7v + 7v + 2v2 + -2v2

Combine like terms: -7v + 7v = 0
2 + 1v + -1v2 = 0 + 2v2 + -2v2
2 + 1v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
2 + 1v + -1v2 = 0

Factor a trinomial.
(2 + -1v)(1 + v) = 0


Subproblem 1
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2

Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + v = 0 + -1
v = 0 + -1

Combine like terms: 0 + -1 = -1
v = -1

Simplifying
v = -1
Solution
v = {2, -1}

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