6x^2+12x=378

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Solution for 6x^2+12x=378 equation:


Simplifying
6x2 + 12x = 378

Reorder the terms:
12x + 6x2 = 378

Solving
12x + 6x2 = 378

Solving for variable 'x'.

Reorder the terms:
-378 + 12x + 6x2 = 378 + -378

Combine like terms: 378 + -378 = 0
-378 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-63 + 2x + x2) = 0

Factor a trinomial.
6((-9 + -1x)(7 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

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

Solution

x = {-9, 7}

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