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

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


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

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

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

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

Combine like terms: 3x + -5x = -2x
4(-15 + -2x + x2) = 0
(-15 * 4 + -2x * 4 + x2 * 4) = 0
(-60 + -8x + 4x2) = 0

Solving
-60 + -8x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -2x + x2) = 0

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

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

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 = {-3, 5}

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