(x+7)(3x-12)=0

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Solution for (x+7)(3x-12)=0 equation:


Simplifying
(x + 7)(3x + -12) = 0

Reorder the terms:
(7 + x)(3x + -12) = 0

Reorder the terms:
(7 + x)(-12 + 3x) = 0

Multiply (7 + x) * (-12 + 3x)
(7(-12 + 3x) + x(-12 + 3x)) = 0
((-12 * 7 + 3x * 7) + x(-12 + 3x)) = 0
((-84 + 21x) + x(-12 + 3x)) = 0
(-84 + 21x + (-12 * x + 3x * x)) = 0
(-84 + 21x + (-12x + 3x2)) = 0

Combine like terms: 21x + -12x = 9x
(-84 + 9x + 3x2) = 0

Solving
-84 + 9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + 3x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-7, 4}

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