-2x^2+6x+8=12

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Solution for -2x^2+6x+8=12 equation:


Simplifying
-2x2 + 6x + 8 = 12

Reorder the terms:
8 + 6x + -2x2 = 12

Solving
8 + 6x + -2x2 = 12

Solving for variable 'x'.

Reorder the terms:
8 + -12 + 6x + -2x2 = 12 + -12

Combine like terms: 8 + -12 = -4
-4 + 6x + -2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-4 + 6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3x + -1x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {2, 1}

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