(4x-12)(2x+5)=0

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Solution for (4x-12)(2x+5)=0 equation:


Simplifying
(4x + -12)(2x + 5) = 0

Reorder the terms:
(-12 + 4x)(2x + 5) = 0

Reorder the terms:
(-12 + 4x)(5 + 2x) = 0

Multiply (-12 + 4x) * (5 + 2x)
(-12(5 + 2x) + 4x * (5 + 2x)) = 0
((5 * -12 + 2x * -12) + 4x * (5 + 2x)) = 0
((-60 + -24x) + 4x * (5 + 2x)) = 0
(-60 + -24x + (5 * 4x + 2x * 4x)) = 0
(-60 + -24x + (20x + 8x2)) = 0

Combine like terms: -24x + 20x = -4x
(-60 + -4x + 8x2) = 0

Solving
-60 + -4x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -1x + 2x2) = 0

Factor a trinomial.
4((-5 + -2x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-2.5, 3}

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