4x(x-4)(x-6)=0

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Solution for 4x(x-4)(x-6)=0 equation: 


Simplifying
4x(x + -4)(x + -6) = 0

Reorder the terms:
4x(-4 + x)(x + -6) = 0

Reorder the terms:
4x(-4 + x)(-6 + x) = 0

Multiply (-4 + x) * (-6 + x)
4x(-4(-6 + x) + x(-6 + x)) = 0
4x((-6 * -4 + x * -4) + x(-6 + x)) = 0
4x((24 + -4x) + x(-6 + x)) = 0
4x(24 + -4x + (-6 * x + x * x)) = 0
4x(24 + -4x + (-6x + x2)) = 0

Combine like terms: -4x + -6x = -10x
4x(24 + -10x + x2) = 0
(24 * 4x + -10x * 4x + x2 * 4x) = 0
(96x + -40x2 + 4x3) = 0

Solving
96x + -40x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(24 + -10x + x2) = 0

Factor a trinomial.
4x((4 + -1x)(6 + -1x)) = 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 '(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 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 4, 6}

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