-4x=2x^2-6

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Solution for -4x=2x^2-6 equation:


Simplifying
-4x = 2x2 + -6

Reorder the terms:
-4x = -6 + 2x2

Solving
-4x = -6 + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -4x + -2x2 = -6 + 2x2 + 6 + -2x2

Reorder the terms:
6 + -4x + -2x2 = -6 + 6 + 2x2 + -2x2

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

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

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

Factor a trinomial.
2((1 + -1x)(3 + x)) = 0

Ignore the factor 2.

Subproblem 1

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

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 = {1, -3}

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