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

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Solution for (2x-3)(4x+8)=0 equation: 


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

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

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

Multiply (-3 + 2x) * (8 + 4x)
(-3(8 + 4x) + 2x * (8 + 4x)) = 0
((8 * -3 + 4x * -3) + 2x * (8 + 4x)) = 0
((-24 + -12x) + 2x * (8 + 4x)) = 0
(-24 + -12x + (8 * 2x + 4x * 2x)) = 0
(-24 + -12x + (16x + 8x2)) = 0

Combine like terms: -12x + 16x = 4x
(-24 + 4x + 8x2) = 0

Solving
-24 + 4x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + 2x2) = 0

Factor a trinomial.
4((-2 + -1x)(3 + -2x)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1.5}

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