-2x=x^2+5x+12

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Solution for -2x=x^2+5x+12 equation:


Simplifying
-2x = x2 + 5x + 12

Reorder the terms:
-2x = 12 + 5x + x2

Solving
-2x = 12 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + -2x + -5x + -1x2 = 12 + 5x + x2 + -12 + -5x + -1x2

Combine like terms: -2x + -5x = -7x
-12 + -7x + -1x2 = 12 + 5x + x2 + -12 + -5x + -1x2

Reorder the terms:
-12 + -7x + -1x2 = 12 + -12 + 5x + -5x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-12 + -7x + -1x2 = 0 + 5x + -5x + x2 + -1x2
-12 + -7x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-12 + -7x + -1x2 = 0 + x2 + -1x2
-12 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7x + x2) = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

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 = {-4, -3}

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