2v^2-16v+32=(v-4)(v-4)

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Solution for 2v^2-16v+32=(v-4)(v-4) equation: 


Simplifying
2v2 + -16v + 32 = (v + -4)(v + -4)

Reorder the terms:
32 + -16v + 2v2 = (v + -4)(v + -4)

Reorder the terms:
32 + -16v + 2v2 = (-4 + v)(v + -4)

Reorder the terms:
32 + -16v + 2v2 = (-4 + v)(-4 + v)

Multiply (-4 + v) * (-4 + v)
32 + -16v + 2v2 = (-4(-4 + v) + v(-4 + v))
32 + -16v + 2v2 = ((-4 * -4 + v * -4) + v(-4 + v))
32 + -16v + 2v2 = ((16 + -4v) + v(-4 + v))
32 + -16v + 2v2 = (16 + -4v + (-4 * v + v * v))
32 + -16v + 2v2 = (16 + -4v + (-4v + v2))

Combine like terms: -4v + -4v = -8v
32 + -16v + 2v2 = (16 + -8v + v2)

Solving
32 + -16v + 2v2 = 16 + -8v + v2

Solving for variable 'v'.

Reorder the terms:
32 + -16 + -16v + 8v + 2v2 + -1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Combine like terms: 32 + -16 = 16
16 + -16v + 8v + 2v2 + -1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Combine like terms: -16v + 8v = -8v
16 + -8v + 2v2 + -1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
16 + -8v + 1v2 = 16 + -8v + v2 + -16 + 8v + -1v2

Reorder the terms:
16 + -8v + 1v2 = 16 + -16 + -8v + 8v + v2 + -1v2

Combine like terms: 16 + -16 = 0
16 + -8v + 1v2 = 0 + -8v + 8v + v2 + -1v2
16 + -8v + 1v2 = -8v + 8v + v2 + -1v2

Combine like terms: -8v + 8v = 0
16 + -8v + 1v2 = 0 + v2 + -1v2
16 + -8v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
16 + -8v + 1v2 = 0

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


Subproblem 1
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

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 = {4, 4}

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