(v-7)(v-7)=2v^2-22v+61

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Solution for (v-7)(v-7)=2v^2-22v+61 equation: 


Simplifying
(v + -7)(v + -7) = 2v2 + -22v + 61

Reorder the terms:
(-7 + v)(v + -7) = 2v2 + -22v + 61

Reorder the terms:
(-7 + v)(-7 + v) = 2v2 + -22v + 61

Multiply (-7 + v) * (-7 + v)
(-7(-7 + v) + v(-7 + v)) = 2v2 + -22v + 61
((-7 * -7 + v * -7) + v(-7 + v)) = 2v2 + -22v + 61
((49 + -7v) + v(-7 + v)) = 2v2 + -22v + 61
(49 + -7v + (-7 * v + v * v)) = 2v2 + -22v + 61
(49 + -7v + (-7v + v2)) = 2v2 + -22v + 61

Combine like terms: -7v + -7v = -14v
(49 + -14v + v2) = 2v2 + -22v + 61

Reorder the terms:
49 + -14v + v2 = 61 + -22v + 2v2

Solving
49 + -14v + v2 = 61 + -22v + 2v2

Solving for variable 'v'.

Reorder the terms:
49 + -61 + -14v + 22v + v2 + -2v2 = 61 + -22v + 2v2 + -61 + 22v + -2v2

Combine like terms: 49 + -61 = -12
-12 + -14v + 22v + v2 + -2v2 = 61 + -22v + 2v2 + -61 + 22v + -2v2

Combine like terms: -14v + 22v = 8v
-12 + 8v + v2 + -2v2 = 61 + -22v + 2v2 + -61 + 22v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-12 + 8v + -1v2 = 61 + -22v + 2v2 + -61 + 22v + -2v2

Reorder the terms:
-12 + 8v + -1v2 = 61 + -61 + -22v + 22v + 2v2 + -2v2

Combine like terms: 61 + -61 = 0
-12 + 8v + -1v2 = 0 + -22v + 22v + 2v2 + -2v2
-12 + 8v + -1v2 = -22v + 22v + 2v2 + -2v2

Combine like terms: -22v + 22v = 0
-12 + 8v + -1v2 = 0 + 2v2 + -2v2
-12 + 8v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-12 + 8v + -1v2 = 0

Factor a trinomial.
(-6 + v)(2 + -1v) = 0


Subproblem 1
Set the factor '(-6 + v)' equal to zero and attempt to solve:

Simplifying
-6 + v = 0

Solving
-6 + v = 0

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

Add '6' to each side of the equation.
-6 + 6 + v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + v = 0 + 6
v = 0 + 6

Combine like terms: 0 + 6 = 6
v = 6

Simplifying
v = 6

Subproblem 2
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
Solution
v = {6, 2}

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