3(2x+1)(2x-3)=-24x

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Solution for 3(2x+1)(2x-3)=-24x equation: 


Simplifying
3(2x + 1)(2x + -3) = -24x

Reorder the terms:
3(1 + 2x)(2x + -3) = -24x

Reorder the terms:
3(1 + 2x)(-3 + 2x) = -24x

Multiply (1 + 2x) * (-3 + 2x)
3(1(-3 + 2x) + 2x * (-3 + 2x)) = -24x
3((-3 * 1 + 2x * 1) + 2x * (-3 + 2x)) = -24x
3((-3 + 2x) + 2x * (-3 + 2x)) = -24x
3(-3 + 2x + (-3 * 2x + 2x * 2x)) = -24x
3(-3 + 2x + (-6x + 4x2)) = -24x

Combine like terms: 2x + -6x = -4x
3(-3 + -4x + 4x2) = -24x
(-3 * 3 + -4x * 3 + 4x2 * 3) = -24x
(-9 + -12x + 12x2) = -24x

Solving
-9 + -12x + 12x2 = -24x

Solving for variable 'x'.

Reorder the terms:
-9 + -12x + 24x + 12x2 = -24x + 24x

Combine like terms: -12x + 24x = 12x
-9 + 12x + 12x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-9 + 12x + 12x2 = 0

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

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

Ignore the factor 3.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.5, 0.5}

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