(v-5)(v-5)=2v^2-16v+18

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Solution for (v-5)(v-5)=2v^2-16v+18 equation: 


Simplifying
(v + -5)(v + -5) = 2v2 + -16v + 18

Reorder the terms:
(-5 + v)(v + -5) = 2v2 + -16v + 18

Reorder the terms:
(-5 + v)(-5 + v) = 2v2 + -16v + 18

Multiply (-5 + v) * (-5 + v)
(-5(-5 + v) + v(-5 + v)) = 2v2 + -16v + 18
((-5 * -5 + v * -5) + v(-5 + v)) = 2v2 + -16v + 18
((25 + -5v) + v(-5 + v)) = 2v2 + -16v + 18
(25 + -5v + (-5 * v + v * v)) = 2v2 + -16v + 18
(25 + -5v + (-5v + v2)) = 2v2 + -16v + 18

Combine like terms: -5v + -5v = -10v
(25 + -10v + v2) = 2v2 + -16v + 18

Reorder the terms:
25 + -10v + v2 = 18 + -16v + 2v2

Solving
25 + -10v + v2 = 18 + -16v + 2v2

Solving for variable 'v'.

Reorder the terms:
25 + -18 + -10v + 16v + v2 + -2v2 = 18 + -16v + 2v2 + -18 + 16v + -2v2

Combine like terms: 25 + -18 = 7
7 + -10v + 16v + v2 + -2v2 = 18 + -16v + 2v2 + -18 + 16v + -2v2

Combine like terms: -10v + 16v = 6v
7 + 6v + v2 + -2v2 = 18 + -16v + 2v2 + -18 + 16v + -2v2

Combine like terms: v2 + -2v2 = -1v2
7 + 6v + -1v2 = 18 + -16v + 2v2 + -18 + 16v + -2v2

Reorder the terms:
7 + 6v + -1v2 = 18 + -18 + -16v + 16v + 2v2 + -2v2

Combine like terms: 18 + -18 = 0
7 + 6v + -1v2 = 0 + -16v + 16v + 2v2 + -2v2
7 + 6v + -1v2 = -16v + 16v + 2v2 + -2v2

Combine like terms: -16v + 16v = 0
7 + 6v + -1v2 = 0 + 2v2 + -2v2
7 + 6v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
7 + 6v + -1v2 = 0

Factor a trinomial.
(7 + -1v)(1 + v) = 0


Subproblem 1
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Solution
v = {7, -1}

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