4(4x+12)(3x-2)=0

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Solution for 4(4x+12)(3x-2)=0 equation: 


Simplifying
4(4x + 12)(3x + -2) = 0

Reorder the terms:
4(12 + 4x)(3x + -2) = 0

Reorder the terms:
4(12 + 4x)(-2 + 3x) = 0

Multiply (12 + 4x) * (-2 + 3x)
4(12(-2 + 3x) + 4x * (-2 + 3x)) = 0
4((-2 * 12 + 3x * 12) + 4x * (-2 + 3x)) = 0
4((-24 + 36x) + 4x * (-2 + 3x)) = 0
4(-24 + 36x + (-2 * 4x + 3x * 4x)) = 0
4(-24 + 36x + (-8x + 12x2)) = 0

Combine like terms: 36x + -8x = 28x
4(-24 + 28x + 12x2) = 0
(-24 * 4 + 28x * 4 + 12x2 * 4) = 0
(-96 + 112x + 48x2) = 0

Solving
-96 + 112x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-6 + 7x + 3x2) = 0

Factor a trinomial.
16((-3 + -1x)(2 + -3x)) = 0

Ignore the factor 16.

Subproblem 1
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 2
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
Solution
x = {-3, 0.6666666667}

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