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

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


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

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

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

Multiply (2 + 3x) * (-3 + 4x)
4(2(-3 + 4x) + 3x * (-3 + 4x)) = 0
4((-3 * 2 + 4x * 2) + 3x * (-3 + 4x)) = 0
4((-6 + 8x) + 3x * (-3 + 4x)) = 0
4(-6 + 8x + (-3 * 3x + 4x * 3x)) = 0
4(-6 + 8x + (-9x + 12x2)) = 0

Combine like terms: 8x + -9x = -1x
4(-6 + -1x + 12x2) = 0
(-6 * 4 + -1x * 4 + 12x2 * 4) = 0
(-24 + -4x + 48x2) = 0

Solving
-24 + -4x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1x + 12x2) = 0

Factor a trinomial.
4((-2 + -3x)(3 + -4x)) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-0.6666666667, 0.75}

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