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

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


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

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

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

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

Combine like terms: 5x + -3x = 2x
-4x(-15 + 2x + x2) = 0
(-15 * -4x + 2x * -4x + x2 * -4x) = 0
(60x + -8x2 + -4x3) = 0

Solving
60x + -8x2 + -4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(15 + -2x + -1x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
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 3
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, 3, -5}

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