-x=2x^2-6

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Solution for -x=2x^2-6 equation:


Simplifying
-1x = 2x2 + -6

Reorder the terms:
-1x = -6 + 2x2

Solving
-1x = -6 + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -1x + -2x2 = -6 + 2x2 + 6 + -2x2

Reorder the terms:
6 + -1x + -2x2 = -6 + 6 + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -1x + -2x2 = 0 + 2x2 + -2x2
6 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -1x + -2x2 = 0

Factor a trinomial.
(3 + -2x)(2 + x) = 0

Subproblem 1

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

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 = {1.5, -2}

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