4x(3x+15)(4x-20)=0

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Solution for 4x(3x+15)(4x-20)=0 equation: 


Simplifying
4x(3x + 15)(4x + -20) = 0

Reorder the terms:
4x(15 + 3x)(4x + -20) = 0

Reorder the terms:
4x(15 + 3x)(-20 + 4x) = 0

Multiply (15 + 3x) * (-20 + 4x)
4x(15(-20 + 4x) + 3x * (-20 + 4x)) = 0
4x((-20 * 15 + 4x * 15) + 3x * (-20 + 4x)) = 0
4x((-300 + 60x) + 3x * (-20 + 4x)) = 0
4x(-300 + 60x + (-20 * 3x + 4x * 3x)) = 0
4x(-300 + 60x + (-60x + 12x2)) = 0

Combine like terms: 60x + -60x = 0
4x(-300 + 0 + 12x2) = 0
4x(-300 + 12x2) = 0
(-300 * 4x + 12x2 * 4x) = 0
(-1200x + 48x3) = 0

Solving
-1200x + 48x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '48x'.
48x(-25 + x2) = 0

Factor a difference between two squares.
48x((5 + x)(-5 + x)) = 0

Ignore the factor 48.

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 '(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

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, -5, 5}

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