4x(3x+4)(x-6)=0

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Solution for 4x(3x+4)(x-6)=0 equation: 


Simplifying
4x(3x + 4)(x + -6) = 0

Reorder the terms:
4x(4 + 3x)(x + -6) = 0

Reorder the terms:
4x(4 + 3x)(-6 + x) = 0

Multiply (4 + 3x) * (-6 + x)
4x(4(-6 + x) + 3x * (-6 + x)) = 0
4x((-6 * 4 + x * 4) + 3x * (-6 + x)) = 0
4x((-24 + 4x) + 3x * (-6 + x)) = 0
4x(-24 + 4x + (-6 * 3x + x * 3x)) = 0
4x(-24 + 4x + (-18x + 3x2)) = 0

Combine like terms: 4x + -18x = -14x
4x(-24 + -14x + 3x2) = 0
(-24 * 4x + -14x * 4x + 3x2 * 4x) = 0
(-96x + -56x2 + 12x3) = 0

Solving
-96x + -56x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-24 + -14x + 3x2) = 0

Factor a trinomial.
4x((-4 + -3x)(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 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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, -1.333333333, 6}

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