(v-4)(v-4)=2v^2-13v+22

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Solution for (v-4)(v-4)=2v^2-13v+22 equation: 


Simplifying
(v + -4)(v + -4) = 2v2 + -13v + 22

Reorder the terms:
(-4 + v)(v + -4) = 2v2 + -13v + 22

Reorder the terms:
(-4 + v)(-4 + v) = 2v2 + -13v + 22

Multiply (-4 + v) * (-4 + v)
(-4(-4 + v) + v(-4 + v)) = 2v2 + -13v + 22
((-4 * -4 + v * -4) + v(-4 + v)) = 2v2 + -13v + 22
((16 + -4v) + v(-4 + v)) = 2v2 + -13v + 22
(16 + -4v + (-4 * v + v * v)) = 2v2 + -13v + 22
(16 + -4v + (-4v + v2)) = 2v2 + -13v + 22

Combine like terms: -4v + -4v = -8v
(16 + -8v + v2) = 2v2 + -13v + 22

Reorder the terms:
16 + -8v + v2 = 22 + -13v + 2v2

Solving
16 + -8v + v2 = 22 + -13v + 2v2

Solving for variable 'v'.

Reorder the terms:
16 + -22 + -8v + 13v + v2 + -2v2 = 22 + -13v + 2v2 + -22 + 13v + -2v2

Combine like terms: 16 + -22 = -6
-6 + -8v + 13v + v2 + -2v2 = 22 + -13v + 2v2 + -22 + 13v + -2v2

Combine like terms: -8v + 13v = 5v
-6 + 5v + v2 + -2v2 = 22 + -13v + 2v2 + -22 + 13v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-6 + 5v + -1v2 = 22 + -13v + 2v2 + -22 + 13v + -2v2

Reorder the terms:
-6 + 5v + -1v2 = 22 + -22 + -13v + 13v + 2v2 + -2v2

Combine like terms: 22 + -22 = 0
-6 + 5v + -1v2 = 0 + -13v + 13v + 2v2 + -2v2
-6 + 5v + -1v2 = -13v + 13v + 2v2 + -2v2

Combine like terms: -13v + 13v = 0
-6 + 5v + -1v2 = 0 + 2v2 + -2v2
-6 + 5v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-6 + 5v + -1v2 = 0

Factor a trinomial.
(-3 + v)(2 + -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 '(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 = {3, 2}

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