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

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


Simplifying
(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 + -1x2) = 0

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

Ignore the factor 12.

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {5, -2}

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