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

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


Simplifying
(-1x + 5)(4x + 12) = 0

Reorder the terms:
(5 + -1x)(4x + 12) = 0

Reorder the terms:
(5 + -1x)(12 + 4x) = 0

Multiply (5 + -1x) * (12 + 4x)
(5(12 + 4x) + -1x * (12 + 4x)) = 0
((12 * 5 + 4x * 5) + -1x * (12 + 4x)) = 0
((60 + 20x) + -1x * (12 + 4x)) = 0
(60 + 20x + (12 * -1x + 4x * -1x)) = 0
(60 + 20x + (-12x + -4x2)) = 0

Combine like terms: 20x + -12x = 8x
(60 + 8x + -4x2) = 0

Solving
60 + 8x + -4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 4.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Subproblem 2

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

Solution

x = {5, -3}

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