(3x+9)(x-8)=0

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Solution for (3x+9)(x-8)=0 equation: 


Simplifying
(3x + 9)(x + -8) = 0

Reorder the terms:
(9 + 3x)(x + -8) = 0

Reorder the terms:
(9 + 3x)(-8 + x) = 0

Multiply (9 + 3x) * (-8 + x)
(9(-8 + x) + 3x * (-8 + x)) = 0
((-8 * 9 + x * 9) + 3x * (-8 + x)) = 0
((-72 + 9x) + 3x * (-8 + x)) = 0
(-72 + 9x + (-8 * 3x + x * 3x)) = 0
(-72 + 9x + (-24x + 3x2)) = 0

Combine like terms: 9x + -24x = -15x
(-72 + -15x + 3x2) = 0

Solving
-72 + -15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -5x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(8 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

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

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

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

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

Simplifying
x = 8
Solution
x = {-3, 8}

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