2(4x-5)(4x+3)=0

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Solution for 2(4x-5)(4x+3)=0 equation:


Simplifying
2(4x + -5)(4x + 3) = 0

Reorder the terms:
2(-5 + 4x)(4x + 3) = 0

Reorder the terms:
2(-5 + 4x)(3 + 4x) = 0

Multiply (-5 + 4x) * (3 + 4x)
2(-5(3 + 4x) + 4x * (3 + 4x)) = 0
2((3 * -5 + 4x * -5) + 4x * (3 + 4x)) = 0
2((-15 + -20x) + 4x * (3 + 4x)) = 0
2(-15 + -20x + (3 * 4x + 4x * 4x)) = 0
2(-15 + -20x + (12x + 16x2)) = 0

Combine like terms: -20x + 12x = -8x
2(-15 + -8x + 16x2) = 0
(-15 * 2 + -8x * 2 + 16x2 * 2) = 0
(-30 + -16x + 32x2) = 0

Solving
-30 + -16x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -8x + 16x2) = 0

Factor a trinomial.
2((-3 + -4x)(5 + -4x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75

Subproblem 2

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Solution

x = {-0.75, 1.25}

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