-8-6n(6n-7)=-2(-7+8n)

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Solution for -8-6n(6n-7)=-2(-7+8n) equation: 


Simplifying
-8 + -6n(6n + -7) = -2(-7 + 8n)

Reorder the terms:
-8 + -6n(-7 + 6n) = -2(-7 + 8n)
-8 + (-7 * -6n + 6n * -6n) = -2(-7 + 8n)
-8 + (42n + -36n2) = -2(-7 + 8n)
-8 + 42n + -36n2 = (-7 * -2 + 8n * -2)
-8 + 42n + -36n2 = (14 + -16n)

Solving
-8 + 42n + -36n2 = 14 + -16n

Solving for variable 'n'.

Reorder the terms:
-8 + -14 + 42n + 16n + -36n2 = 14 + -16n + -14 + 16n

Combine like terms: -8 + -14 = -22
-22 + 42n + 16n + -36n2 = 14 + -16n + -14 + 16n

Combine like terms: 42n + 16n = 58n
-22 + 58n + -36n2 = 14 + -16n + -14 + 16n

Reorder the terms:
-22 + 58n + -36n2 = 14 + -14 + -16n + 16n

Combine like terms: 14 + -14 = 0
-22 + 58n + -36n2 = 0 + -16n + 16n
-22 + 58n + -36n2 = -16n + 16n

Combine like terms: -16n + 16n = 0
-22 + 58n + -36n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 29n + -18n2) = 0

Factor a trinomial.
2((-1 + n)(11 + -18n)) = 0

Ignore the factor 2.

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

Simplifying
-1 + n = 0

Solving
-1 + n = 0

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

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

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

Combine like terms: 0 + 1 = 1
n = 1

Simplifying
n = 1

Subproblem 2
Set the factor '(11 + -18n)' equal to zero and attempt to solve:

Simplifying
11 + -18n = 0

Solving
11 + -18n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -18n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -18n = 0 + -11
-18n = 0 + -11

Combine like terms: 0 + -11 = -11
-18n = -11

Divide each side by '-18'.
n = 0.6111111111

Simplifying
n = 0.6111111111
Solution
n = {1, 0.6111111111}

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