2v^2-20v+43=(v-6)(v-6)

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Solution for 2v^2-20v+43=(v-6)(v-6) equation: 


Simplifying
2v2 + -20v + 43 = (v + -6)(v + -6)

Reorder the terms:
43 + -20v + 2v2 = (v + -6)(v + -6)

Reorder the terms:
43 + -20v + 2v2 = (-6 + v)(v + -6)

Reorder the terms:
43 + -20v + 2v2 = (-6 + v)(-6 + v)

Multiply (-6 + v) * (-6 + v)
43 + -20v + 2v2 = (-6(-6 + v) + v(-6 + v))
43 + -20v + 2v2 = ((-6 * -6 + v * -6) + v(-6 + v))
43 + -20v + 2v2 = ((36 + -6v) + v(-6 + v))
43 + -20v + 2v2 = (36 + -6v + (-6 * v + v * v))
43 + -20v + 2v2 = (36 + -6v + (-6v + v2))

Combine like terms: -6v + -6v = -12v
43 + -20v + 2v2 = (36 + -12v + v2)

Solving
43 + -20v + 2v2 = 36 + -12v + v2

Solving for variable 'v'.

Reorder the terms:
43 + -36 + -20v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: 43 + -36 = 7
7 + -20v + 12v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: -20v + 12v = -8v
7 + -8v + 2v2 + -1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
7 + -8v + 1v2 = 36 + -12v + v2 + -36 + 12v + -1v2

Reorder the terms:
7 + -8v + 1v2 = 36 + -36 + -12v + 12v + v2 + -1v2

Combine like terms: 36 + -36 = 0
7 + -8v + 1v2 = 0 + -12v + 12v + v2 + -1v2
7 + -8v + 1v2 = -12v + 12v + v2 + -1v2

Combine like terms: -12v + 12v = 0
7 + -8v + 1v2 = 0 + v2 + -1v2
7 + -8v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
7 + -8v + 1v2 = 0

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


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

Simplifying
1 + -1v = 0

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

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

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

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

Simplifying
v = 1

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 = {1, 7}

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