11v^2-51v-32=8+4v^2

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Solution for 11v^2-51v-32=8+4v^2 equation:


Simplifying
11v2 + -51v + -32 = 8 + 4v2

Reorder the terms:
-32 + -51v + 11v2 = 8 + 4v2

Solving
-32 + -51v + 11v2 = 8 + 4v2

Solving for variable 'v'.

Reorder the terms:
-32 + -8 + -51v + 11v2 + -4v2 = 8 + 4v2 + -8 + -4v2

Combine like terms: -32 + -8 = -40
-40 + -51v + 11v2 + -4v2 = 8 + 4v2 + -8 + -4v2

Combine like terms: 11v2 + -4v2 = 7v2
-40 + -51v + 7v2 = 8 + 4v2 + -8 + -4v2

Reorder the terms:
-40 + -51v + 7v2 = 8 + -8 + 4v2 + -4v2

Combine like terms: 8 + -8 = 0
-40 + -51v + 7v2 = 0 + 4v2 + -4v2
-40 + -51v + 7v2 = 4v2 + -4v2

Combine like terms: 4v2 + -4v2 = 0
-40 + -51v + 7v2 = 0

Factor a trinomial.
(-5 + -7v)(8 + -1v) = 0


Subproblem 1
Set the factor '(-5 + -7v)' equal to zero and attempt to solve:

Simplifying
-5 + -7v = 0

Solving
-5 + -7v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -7v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7v = 0 + 5
-7v = 0 + 5

Combine like terms: 0 + 5 = 5
-7v = 5

Divide each side by '-7'.
v = -0.7142857143

Simplifying
v = -0.7142857143

Subproblem 2
Set the factor '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1v = 0 + -8

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

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

Divide each side by '-1'.
v = 8

Simplifying
v = 8
Solution
v = {-0.7142857143, 8}

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