(5x+20)(3x-15)=0

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Solution for (5x+20)(3x-15)=0 equation:


Simplifying
(5x + 20)(3x + -15) = 0

Reorder the terms:
(20 + 5x)(3x + -15) = 0

Reorder the terms:
(20 + 5x)(-15 + 3x) = 0

Multiply (20 + 5x) * (-15 + 3x)
(20(-15 + 3x) + 5x * (-15 + 3x)) = 0
((-15 * 20 + 3x * 20) + 5x * (-15 + 3x)) = 0
((-300 + 60x) + 5x * (-15 + 3x)) = 0
(-300 + 60x + (-15 * 5x + 3x * 5x)) = 0
(-300 + 60x + (-75x + 15x2)) = 0

Combine like terms: 60x + -75x = -15x
(-300 + -15x + 15x2) = 0

Solving
-300 + -15x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-20 + -1x + x2) = 0

Factor a trinomial.
15((-4 + -1x)(5 + -1x)) = 0

Ignore the factor 15.

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 '(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 = {-4, 5}

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