(v-4)(v-4)=2v^2-18v+40

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Solution for (v-4)(v-4)=2v^2-18v+40 equation: 


Simplifying
(v + -4)(v + -4) = 2v2 + -18v + 40

Reorder the terms:
(-4 + v)(v + -4) = 2v2 + -18v + 40

Reorder the terms:
(-4 + v)(-4 + v) = 2v2 + -18v + 40

Multiply (-4 + v) * (-4 + v)
(-4(-4 + v) + v(-4 + v)) = 2v2 + -18v + 40
((-4 * -4 + v * -4) + v(-4 + v)) = 2v2 + -18v + 40
((16 + -4v) + v(-4 + v)) = 2v2 + -18v + 40
(16 + -4v + (-4 * v + v * v)) = 2v2 + -18v + 40
(16 + -4v + (-4v + v2)) = 2v2 + -18v + 40

Combine like terms: -4v + -4v = -8v
(16 + -8v + v2) = 2v2 + -18v + 40

Reorder the terms:
16 + -8v + v2 = 40 + -18v + 2v2

Solving
16 + -8v + v2 = 40 + -18v + 2v2

Solving for variable 'v'.

Reorder the terms:
16 + -40 + -8v + 18v + v2 + -2v2 = 40 + -18v + 2v2 + -40 + 18v + -2v2

Combine like terms: 16 + -40 = -24
-24 + -8v + 18v + v2 + -2v2 = 40 + -18v + 2v2 + -40 + 18v + -2v2

Combine like terms: -8v + 18v = 10v
-24 + 10v + v2 + -2v2 = 40 + -18v + 2v2 + -40 + 18v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-24 + 10v + -1v2 = 40 + -18v + 2v2 + -40 + 18v + -2v2

Reorder the terms:
-24 + 10v + -1v2 = 40 + -40 + -18v + 18v + 2v2 + -2v2

Combine like terms: 40 + -40 = 0
-24 + 10v + -1v2 = 0 + -18v + 18v + 2v2 + -2v2
-24 + 10v + -1v2 = -18v + 18v + 2v2 + -2v2

Combine like terms: -18v + 18v = 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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