(3x-12)(20+4x)=0

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Solution for (3x-12)(20+4x)=0 equation: 


Simplifying
(3x + -12)(20 + 4x) = 0

Reorder the terms:
(-12 + 3x)(20 + 4x) = 0

Multiply (-12 + 3x) * (20 + 4x)
(-12(20 + 4x) + 3x * (20 + 4x)) = 0
((20 * -12 + 4x * -12) + 3x * (20 + 4x)) = 0
((-240 + -48x) + 3x * (20 + 4x)) = 0
(-240 + -48x + (20 * 3x + 4x * 3x)) = 0
(-240 + -48x + (60x + 12x2)) = 0

Combine like terms: -48x + 60x = 12x
(-240 + 12x + 12x2) = 0

Solving
-240 + 12x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-20 + x + x2) = 0

Factor a trinomial.
12((-5 + -1x)(4 + -1x)) = 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 '(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
Solution
x = {-5, 4}

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