(3x-15)(8+4x)=0

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Solution for (3x-15)(8+4x)=0 equation: 


Simplifying
(3x + -15)(8 + 4x) = 0

Reorder the terms:
(-15 + 3x)(8 + 4x) = 0

Multiply (-15 + 3x) * (8 + 4x)
(-15(8 + 4x) + 3x * (8 + 4x)) = 0
((8 * -15 + 4x * -15) + 3x * (8 + 4x)) = 0
((-120 + -60x) + 3x * (8 + 4x)) = 0
(-120 + -60x + (8 * 3x + 4x * 3x)) = 0
(-120 + -60x + (24x + 12x2)) = 0

Combine like terms: -60x + 24x = -36x
(-120 + -36x + 12x2) = 0

Solving
-120 + -36x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-10 + -3x + x2) = 0

Factor a trinomial.
12((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 12.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

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

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

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

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

Simplifying
x = -2

Subproblem 2
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
Solution
x = {-2, 5}

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