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

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


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

Reorder the terms:
8x(3 + 2x) = 4x(2x + -3)
(3 * 8x + 2x * 8x) = 4x(2x + -3)
(24x + 16x2) = 4x(2x + -3)

Reorder the terms:
24x + 16x2 = 4x(-3 + 2x)
24x + 16x2 = (-3 * 4x + 2x * 4x)
24x + 16x2 = (-12x + 8x2)

Solving
24x + 16x2 = -12x + 8x2

Solving for variable 'x'.

Reorder the terms:
24x + 12x + 16x2 + -8x2 = -12x + 8x2 + 12x + -8x2

Combine like terms: 24x + 12x = 36x
36x + 16x2 + -8x2 = -12x + 8x2 + 12x + -8x2

Combine like terms: 16x2 + -8x2 = 8x2
36x + 8x2 = -12x + 8x2 + 12x + -8x2

Reorder the terms:
36x + 8x2 = -12x + 12x + 8x2 + -8x2

Combine like terms: -12x + 12x = 0
36x + 8x2 = 0 + 8x2 + -8x2
36x + 8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
36x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(9 + 2x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve:

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {0, -4.5}

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