(5x-20)(3x+4)=0

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Solution for (5x-20)(3x+4)=0 equation: 


Simplifying
(5x + -20)(3x + 4) = 0

Reorder the terms:
(-20 + 5x)(3x + 4) = 0

Reorder the terms:
(-20 + 5x)(4 + 3x) = 0

Multiply (-20 + 5x) * (4 + 3x)
(-20(4 + 3x) + 5x * (4 + 3x)) = 0
((4 * -20 + 3x * -20) + 5x * (4 + 3x)) = 0
((-80 + -60x) + 5x * (4 + 3x)) = 0
(-80 + -60x + (4 * 5x + 3x * 5x)) = 0
(-80 + -60x + (20x + 15x2)) = 0

Combine like terms: -60x + 20x = -40x
(-80 + -40x + 15x2) = 0

Solving
-80 + -40x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -8x + 3x2) = 0

Factor a trinomial.
5((-4 + -3x)(4 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 4}

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