(4n+8)(8n-7)=

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Solution for (4n+8)(8n-7)= equation: 


Simplifying
(4n + 8)(8n + -7) = 0

Reorder the terms:
(8 + 4n)(8n + -7) = 0

Reorder the terms:
(8 + 4n)(-7 + 8n) = 0

Multiply (8 + 4n) * (-7 + 8n)
(8(-7 + 8n) + 4n * (-7 + 8n)) = 0
((-7 * 8 + 8n * 8) + 4n * (-7 + 8n)) = 0
((-56 + 64n) + 4n * (-7 + 8n)) = 0
(-56 + 64n + (-7 * 4n + 8n * 4n)) = 0
(-56 + 64n + (-28n + 32n2)) = 0

Combine like terms: 64n + -28n = 36n
(-56 + 36n + 32n2) = 0

Solving
-56 + 36n + 32n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 9n + 8n2) = 0

Factor a trinomial.
4((-2 + -1n)(7 + -8n)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2

Subproblem 2
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
Solution
n = {-2, 0.875}

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