(v-6)(v-6)=2v^2-11v+30

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Solution for (v-6)(v-6)=2v^2-11v+30 equation: 


Simplifying
(v + -6)(v + -6) = 2v2 + -11v + 30

Reorder the terms:
(-6 + v)(v + -6) = 2v2 + -11v + 30

Reorder the terms:
(-6 + v)(-6 + v) = 2v2 + -11v + 30

Multiply (-6 + v) * (-6 + v)
(-6(-6 + v) + v(-6 + v)) = 2v2 + -11v + 30
((-6 * -6 + v * -6) + v(-6 + v)) = 2v2 + -11v + 30
((36 + -6v) + v(-6 + v)) = 2v2 + -11v + 30
(36 + -6v + (-6 * v + v * v)) = 2v2 + -11v + 30
(36 + -6v + (-6v + v2)) = 2v2 + -11v + 30

Combine like terms: -6v + -6v = -12v
(36 + -12v + v2) = 2v2 + -11v + 30

Reorder the terms:
36 + -12v + v2 = 30 + -11v + 2v2

Solving
36 + -12v + v2 = 30 + -11v + 2v2

Solving for variable 'v'.

Reorder the terms:
36 + -30 + -12v + 11v + v2 + -2v2 = 30 + -11v + 2v2 + -30 + 11v + -2v2

Combine like terms: 36 + -30 = 6
6 + -12v + 11v + v2 + -2v2 = 30 + -11v + 2v2 + -30 + 11v + -2v2

Combine like terms: -12v + 11v = -1v
6 + -1v + v2 + -2v2 = 30 + -11v + 2v2 + -30 + 11v + -2v2

Combine like terms: v2 + -2v2 = -1v2
6 + -1v + -1v2 = 30 + -11v + 2v2 + -30 + 11v + -2v2

Reorder the terms:
6 + -1v + -1v2 = 30 + -30 + -11v + 11v + 2v2 + -2v2

Combine like terms: 30 + -30 = 0
6 + -1v + -1v2 = 0 + -11v + 11v + 2v2 + -2v2
6 + -1v + -1v2 = -11v + 11v + 2v2 + -2v2

Combine like terms: -11v + 11v = 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.
(2 + -1v)(3 + 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 '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

Solving
3 + v = 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 + v = 0 + -3

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

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

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

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