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

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}