v^2-12v+36=2v^2-v+64

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Solution for v^2-12v+36=2v^2-v+64 equation:


Simplifying
v2 + -12v + 36 = 2v2 + -1v + 64

Reorder the terms:
36 + -12v + v2 = 2v2 + -1v + 64

Reorder the terms:
36 + -12v + v2 = 64 + -1v + 2v2

Solving
36 + -12v + v2 = 64 + -1v + 2v2

Solving for variable 'v'.

Reorder the terms:
36 + -64 + -12v + v + v2 + -2v2 = 64 + -1v + 2v2 + -64 + v + -2v2

Combine like terms: 36 + -64 = -28
-28 + -12v + v + v2 + -2v2 = 64 + -1v + 2v2 + -64 + v + -2v2

Combine like terms: -12v + v = -11v
-28 + -11v + v2 + -2v2 = 64 + -1v + 2v2 + -64 + v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-28 + -11v + -1v2 = 64 + -1v + 2v2 + -64 + v + -2v2

Reorder the terms:
-28 + -11v + -1v2 = 64 + -64 + -1v + v + 2v2 + -2v2

Combine like terms: 64 + -64 = 0
-28 + -11v + -1v2 = 0 + -1v + v + 2v2 + -2v2
-28 + -11v + -1v2 = -1v + v + 2v2 + -2v2

Combine like terms: -1v + v = 0
-28 + -11v + -1v2 = 0 + 2v2 + -2v2
-28 + -11v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-28 + -11v + -1v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 11v + v2) = 0

Factor a trinomial.
-1((7 + v)(4 + v)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7

Subproblem 2

Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4

Solution

v = {-7, -4}

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