(3x-18)(8x+32)=0

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Solution for (3x-18)(8x+32)=0 equation: 


Simplifying
(3x + -18)(8x + 32) = 0

Reorder the terms:
(-18 + 3x)(8x + 32) = 0

Reorder the terms:
(-18 + 3x)(32 + 8x) = 0

Multiply (-18 + 3x) * (32 + 8x)
(-18(32 + 8x) + 3x * (32 + 8x)) = 0
((32 * -18 + 8x * -18) + 3x * (32 + 8x)) = 0
((-576 + -144x) + 3x * (32 + 8x)) = 0
(-576 + -144x + (32 * 3x + 8x * 3x)) = 0
(-576 + -144x + (96x + 24x2)) = 0

Combine like terms: -144x + 96x = -48x
(-576 + -48x + 24x2) = 0

Solving
-576 + -48x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(-24 + -2x + x2) = 0

Factor a trinomial.
24((-4 + -1x)(6 + -1x)) = 0

Ignore the factor 24.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4, 6}

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