(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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