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((-1 + -2x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.5, 1.5}

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