(v-6)(v-6)=2(v-6)(v-5)

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Solution for (v-6)(v-6)=2(v-6)(v-5) equation: 


Simplifying
(v + -6)(v + -6) = 2(v + -6)(v + -5)

Reorder the terms:
(-6 + v)(v + -6) = 2(v + -6)(v + -5)

Reorder the terms:
(-6 + v)(-6 + v) = 2(v + -6)(v + -5)

Multiply (-6 + v) * (-6 + v)
(-6(-6 + v) + v(-6 + v)) = 2(v + -6)(v + -5)
((-6 * -6 + v * -6) + v(-6 + v)) = 2(v + -6)(v + -5)
((36 + -6v) + v(-6 + v)) = 2(v + -6)(v + -5)
(36 + -6v + (-6 * v + v * v)) = 2(v + -6)(v + -5)
(36 + -6v + (-6v + v2)) = 2(v + -6)(v + -5)

Combine like terms: -6v + -6v = -12v
(36 + -12v + v2) = 2(v + -6)(v + -5)

Reorder the terms:
36 + -12v + v2 = 2(-6 + v)(v + -5)

Reorder the terms:
36 + -12v + v2 = 2(-6 + v)(-5 + v)

Multiply (-6 + v) * (-5 + v)
36 + -12v + v2 = 2(-6(-5 + v) + v(-5 + v))
36 + -12v + v2 = 2((-5 * -6 + v * -6) + v(-5 + v))
36 + -12v + v2 = 2((30 + -6v) + v(-5 + v))
36 + -12v + v2 = 2(30 + -6v + (-5 * v + v * v))
36 + -12v + v2 = 2(30 + -6v + (-5v + v2))

Combine like terms: -6v + -5v = -11v
36 + -12v + v2 = 2(30 + -11v + v2)
36 + -12v + v2 = (30 * 2 + -11v * 2 + v2 * 2)
36 + -12v + v2 = (60 + -22v + 2v2)

Solving
36 + -12v + v2 = 60 + -22v + 2v2

Solving for variable 'v'.

Reorder the terms:
36 + -60 + -12v + 22v + v2 + -2v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2

Combine like terms: 36 + -60 = -24
-24 + -12v + 22v + v2 + -2v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2

Combine like terms: -12v + 22v = 10v
-24 + 10v + v2 + -2v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-24 + 10v + -1v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2

Reorder the terms:
-24 + 10v + -1v2 = 60 + -60 + -22v + 22v + 2v2 + -2v2

Combine like terms: 60 + -60 = 0
-24 + 10v + -1v2 = 0 + -22v + 22v + 2v2 + -2v2
-24 + 10v + -1v2 = -22v + 22v + 2v2 + -2v2

Combine like terms: -22v + 22v = 0
-24 + 10v + -1v2 = 0 + 2v2 + -2v2
-24 + 10v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-24 + 10v + -1v2 = 0

Factor a trinomial.
(-6 + v)(4 + -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 '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 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 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {6, 4}

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