(v-3)(v-3)=2v^2-10v+12

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Solution for (v-3)(v-3)=2v^2-10v+12 equation: 


Simplifying
(v + -3)(v + -3) = 2v2 + -10v + 12

Reorder the terms:
(-3 + v)(v + -3) = 2v2 + -10v + 12

Reorder the terms:
(-3 + v)(-3 + v) = 2v2 + -10v + 12

Multiply (-3 + v) * (-3 + v)
(-3(-3 + v) + v(-3 + v)) = 2v2 + -10v + 12
((-3 * -3 + v * -3) + v(-3 + v)) = 2v2 + -10v + 12
((9 + -3v) + v(-3 + v)) = 2v2 + -10v + 12
(9 + -3v + (-3 * v + v * v)) = 2v2 + -10v + 12
(9 + -3v + (-3v + v2)) = 2v2 + -10v + 12

Combine like terms: -3v + -3v = -6v
(9 + -6v + v2) = 2v2 + -10v + 12

Reorder the terms:
9 + -6v + v2 = 12 + -10v + 2v2

Solving
9 + -6v + v2 = 12 + -10v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + -12 + -6v + 10v + v2 + -2v2 = 12 + -10v + 2v2 + -12 + 10v + -2v2

Combine like terms: 9 + -12 = -3
-3 + -6v + 10v + v2 + -2v2 = 12 + -10v + 2v2 + -12 + 10v + -2v2

Combine like terms: -6v + 10v = 4v
-3 + 4v + v2 + -2v2 = 12 + -10v + 2v2 + -12 + 10v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-3 + 4v + -1v2 = 12 + -10v + 2v2 + -12 + 10v + -2v2

Reorder the terms:
-3 + 4v + -1v2 = 12 + -12 + -10v + 10v + 2v2 + -2v2

Combine like terms: 12 + -12 = 0
-3 + 4v + -1v2 = 0 + -10v + 10v + 2v2 + -2v2
-3 + 4v + -1v2 = -10v + 10v + 2v2 + -2v2

Combine like terms: -10v + 10v = 0
-3 + 4v + -1v2 = 0 + 2v2 + -2v2
-3 + 4v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-3 + 4v + -1v2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1
Solution
v = {3, 1}

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