(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 + -1x + 2x2) = 0

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

Ignore the factor 4.

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 '(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
Solution
x = {-1.5, 2}

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