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

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


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

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

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

Multiply (-3 + x) * (-4 + x)
4x((-3(-4 + x) + x(-4 + x))) = 0
4x(((-4 * -3 + x * -3) + x(-4 + x))) = 0
4x(((12 + -3x) + x(-4 + x))) = 0
4x((12 + -3x + (-4 * x + x * x))) = 0
4x((12 + -3x + (-4x + x2))) = 0

Combine like terms: -3x + -4x = -7x
4x((12 + -7x + x2)) = 0
(12 * 4x + -7x * 4x + x2 * 4x) = 0
(48x + -28x2 + 4x3) = 0

Solving
48x + -28x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(12 + -7x + x2) = 0

Factor a trinomial.
4x((3 + -1x)(4 + -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 '(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 '(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
Solution
x = {0, 3, 4}

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