4(3x+2)(x-6)=0

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Solution for 4(3x+2)(x-6)=0 equation: 


Simplifying
4(3x + 2)(x + -6) = 0

Reorder the terms:
4(2 + 3x)(x + -6) = 0

Reorder the terms:
4(2 + 3x)(-6 + x) = 0

Multiply (2 + 3x) * (-6 + x)
4(2(-6 + x) + 3x * (-6 + x)) = 0
4((-6 * 2 + x * 2) + 3x * (-6 + x)) = 0
4((-12 + 2x) + 3x * (-6 + x)) = 0
4(-12 + 2x + (-6 * 3x + x * 3x)) = 0
4(-12 + 2x + (-18x + 3x2)) = 0

Combine like terms: 2x + -18x = -16x
4(-12 + -16x + 3x2) = 0
(-12 * 4 + -16x * 4 + 3x2 * 4) = 0
(-48 + -64x + 12x2) = 0

Solving
-48 + -64x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -16x + 3x2) = 0

Factor a trinomial.
4((-2 + -3x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
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 = {-0.6666666667, 6}

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