-2x^2-6=-3x^2-x

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Solution for -2x^2-6=-3x^2-x equation:


Simplifying
-2x2 + -6 = -3x2 + -1x

Reorder the terms:
-6 + -2x2 = -3x2 + -1x

Reorder the terms:
-6 + -2x2 = -1x + -3x2

Solving
-6 + -2x2 = -1x + -3x2

Solving for variable 'x'.

Reorder the terms:
-6 + x + -2x2 + 3x2 = -1x + -3x2 + x + 3x2

Combine like terms: -2x2 + 3x2 = 1x2
-6 + x + 1x2 = -1x + -3x2 + x + 3x2

Reorder the terms:
-6 + x + 1x2 = -1x + x + -3x2 + 3x2

Combine like terms: -1x + x = 0
-6 + x + 1x2 = 0 + -3x2 + 3x2
-6 + x + 1x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-6 + x + 1x2 = 0

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

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

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 = {-3, 2}

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