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

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


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

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

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

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

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

Solving
-12 + -16x + 16x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 4.

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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