4(2x+3)3(3x-8)=

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Solution for 4(2x+3)3(3x-8)= equation: 


Simplifying
4(2x + 3) * 3(3x + -8) = 0

Reorder the terms:
4(3 + 2x) * 3(3x + -8) = 0

Reorder the terms:
4(3 + 2x) * 3(-8 + 3x) = 0

Reorder the terms for easier multiplication:
4 * 3(3 + 2x)(-8 + 3x) = 0

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

Multiply (3 + 2x) * (-8 + 3x)
12(3(-8 + 3x) + 2x * (-8 + 3x)) = 0
12((-8 * 3 + 3x * 3) + 2x * (-8 + 3x)) = 0
12((-24 + 9x) + 2x * (-8 + 3x)) = 0
12(-24 + 9x + (-8 * 2x + 3x * 2x)) = 0
12(-24 + 9x + (-16x + 6x2)) = 0

Combine like terms: 9x + -16x = -7x
12(-24 + -7x + 6x2) = 0
(-24 * 12 + -7x * 12 + 6x2 * 12) = 0
(-288 + -84x + 72x2) = 0

Solving
-288 + -84x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-24 + -7x + 6x2) = 0

Factor a trinomial.
12((-3 + -2x)(8 + -3x)) = 0

Ignore the factor 12.

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

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-1.5, 2.666666667}

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