(3x-9)(x+1)=96

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Solution for (3x-9)(x+1)=96 equation: 


Simplifying
(3x + -9)(x + 1) = 96

Reorder the terms:
(-9 + 3x)(x + 1) = 96

Reorder the terms:
(-9 + 3x)(1 + x) = 96

Multiply (-9 + 3x) * (1 + x)
(-9(1 + x) + 3x * (1 + x)) = 96
((1 * -9 + x * -9) + 3x * (1 + x)) = 96
((-9 + -9x) + 3x * (1 + x)) = 96
(-9 + -9x + (1 * 3x + x * 3x)) = 96
(-9 + -9x + (3x + 3x2)) = 96

Combine like terms: -9x + 3x = -6x
(-9 + -6x + 3x2) = 96

Solving
-9 + -6x + 3x2 = 96

Solving for variable 'x'.

Reorder the terms:
-9 + -96 + -6x + 3x2 = 96 + -96

Combine like terms: -9 + -96 = -105
-105 + -6x + 3x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-105 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + -2x + x2) = 0

Factor a trinomial.
3((-5 + -1x)(7 + -1x)) = 0

Ignore the factor 3.

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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