2v^2-20v+42=(v-7)2

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Solution for 2v^2-20v+42=(v-7)2 equation: 


Simplifying
2v2 + -20v + 42 = (v + -7) * 2

Reorder the terms:
42 + -20v + 2v2 = (v + -7) * 2

Reorder the terms:
42 + -20v + 2v2 = (-7 + v) * 2

Reorder the terms for easier multiplication:
42 + -20v + 2v2 = 2(-7 + v)
42 + -20v + 2v2 = (-7 * 2 + v * 2)
42 + -20v + 2v2 = (-14 + 2v)

Solving
42 + -20v + 2v2 = -14 + 2v

Solving for variable 'v'.

Reorder the terms:
42 + 14 + -20v + -2v + 2v2 = -14 + 2v + 14 + -2v

Combine like terms: 42 + 14 = 56
56 + -20v + -2v + 2v2 = -14 + 2v + 14 + -2v

Combine like terms: -20v + -2v = -22v
56 + -22v + 2v2 = -14 + 2v + 14 + -2v

Reorder the terms:
56 + -22v + 2v2 = -14 + 14 + 2v + -2v

Combine like terms: -14 + 14 = 0
56 + -22v + 2v2 = 0 + 2v + -2v
56 + -22v + 2v2 = 2v + -2v

Combine like terms: 2v + -2v = 0
56 + -22v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -11v + v2) = 0

Factor a trinomial.
2((4 + -1v)(7 + -1v)) = 0

Ignore the factor 2.

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 '(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
Solution
v = {4, 7}

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