(8n+7)(9n-9)=0

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Solution for (8n+7)(9n-9)=0 equation: 


Simplifying
(8n + 7)(9n + -9) = 0

Reorder the terms:
(7 + 8n)(9n + -9) = 0

Reorder the terms:
(7 + 8n)(-9 + 9n) = 0

Multiply (7 + 8n) * (-9 + 9n)
(7(-9 + 9n) + 8n * (-9 + 9n)) = 0
((-9 * 7 + 9n * 7) + 8n * (-9 + 9n)) = 0
((-63 + 63n) + 8n * (-9 + 9n)) = 0
(-63 + 63n + (-9 * 8n + 9n * 8n)) = 0
(-63 + 63n + (-72n + 72n2)) = 0

Combine like terms: 63n + -72n = -9n
(-63 + -9n + 72n2) = 0

Solving
-63 + -9n + 72n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-7 + -1n + 8n2) = 0

Factor a trinomial.
9((-7 + -8n)(1 + -1n)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-7 + -8n)' equal to zero and attempt to solve:

Simplifying
-7 + -8n = 0

Solving
-7 + -8n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -8n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8n = 0 + 7
-8n = 0 + 7

Combine like terms: 0 + 7 = 7
-8n = 7

Divide each side by '-8'.
n = -0.875

Simplifying
n = -0.875

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-0.875, 1}

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