x^2+6x=2x+12

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Solution for x^2+6x=2x+12 equation:


Simplifying
x2 + 6x = 2x + 12

Reorder the terms:
6x + x2 = 2x + 12

Reorder the terms:
6x + x2 = 12 + 2x

Solving
6x + x2 = 12 + 2x

Solving for variable 'x'.

Reorder the terms:
-12 + 6x + -2x + x2 = 12 + 2x + -12 + -2x

Combine like terms: 6x + -2x = 4x
-12 + 4x + x2 = 12 + 2x + -12 + -2x

Reorder the terms:
-12 + 4x + x2 = 12 + -12 + 2x + -2x

Combine like terms: 12 + -12 = 0
-12 + 4x + x2 = 0 + 2x + -2x
-12 + 4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-6, 2}

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