(v-7)(v-7)=2v^2-15v+43

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Solution for (v-7)(v-7)=2v^2-15v+43 equation: 


Simplifying
(v + -7)(v + -7) = 2v2 + -15v + 43

Reorder the terms:
(-7 + v)(v + -7) = 2v2 + -15v + 43

Reorder the terms:
(-7 + v)(-7 + v) = 2v2 + -15v + 43

Multiply (-7 + v) * (-7 + v)
(-7(-7 + v) + v(-7 + v)) = 2v2 + -15v + 43
((-7 * -7 + v * -7) + v(-7 + v)) = 2v2 + -15v + 43
((49 + -7v) + v(-7 + v)) = 2v2 + -15v + 43
(49 + -7v + (-7 * v + v * v)) = 2v2 + -15v + 43
(49 + -7v + (-7v + v2)) = 2v2 + -15v + 43

Combine like terms: -7v + -7v = -14v
(49 + -14v + v2) = 2v2 + -15v + 43

Reorder the terms:
49 + -14v + v2 = 43 + -15v + 2v2

Solving
49 + -14v + v2 = 43 + -15v + 2v2

Solving for variable 'v'.

Reorder the terms:
49 + -43 + -14v + 15v + v2 + -2v2 = 43 + -15v + 2v2 + -43 + 15v + -2v2

Combine like terms: 49 + -43 = 6
6 + -14v + 15v + v2 + -2v2 = 43 + -15v + 2v2 + -43 + 15v + -2v2

Combine like terms: -14v + 15v = 1v
6 + 1v + v2 + -2v2 = 43 + -15v + 2v2 + -43 + 15v + -2v2

Combine like terms: v2 + -2v2 = -1v2
6 + 1v + -1v2 = 43 + -15v + 2v2 + -43 + 15v + -2v2

Reorder the terms:
6 + 1v + -1v2 = 43 + -43 + -15v + 15v + 2v2 + -2v2

Combine like terms: 43 + -43 = 0
6 + 1v + -1v2 = 0 + -15v + 15v + 2v2 + -2v2
6 + 1v + -1v2 = -15v + 15v + 2v2 + -2v2

Combine like terms: -15v + 15v = 0
6 + 1v + -1v2 = 0 + 2v2 + -2v2
6 + 1v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
6 + 1v + -1v2 = 0

Factor a trinomial.
(3 + -1v)(2 + v) = 0


Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3

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

Simplifying
2 + v = 0

Solving
2 + v = 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 + v = 0 + -2

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

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

Simplifying
v = -2
Solution
v = {3, -2}

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