12(x+2)(x+7)=0

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Solution for 12(x+2)(x+7)=0 equation:


Simplifying
12(x + 2)(x + 7) = 0

Reorder the terms:
12(2 + x)(x + 7) = 0

Reorder the terms:
12(2 + x)(7 + x) = 0

Multiply (2 + x) * (7 + x)
12(2(7 + x) + x(7 + x)) = 0
12((7 * 2 + x * 2) + x(7 + x)) = 0
12((14 + 2x) + x(7 + x)) = 0
12(14 + 2x + (7 * x + x * x)) = 0
12(14 + 2x + (7x + x2)) = 0

Combine like terms: 2x + 7x = 9x
12(14 + 9x + x2) = 0
(14 * 12 + 9x * 12 + x2 * 12) = 0
(168 + 108x + 12x2) = 0

Solving
168 + 108x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(14 + 9x + x2) = 0

Factor a trinomial.
12((7 + x)(2 + x)) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {-7, -2}

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