-x^2=-2x-3

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


Simplifying
-1x2 = -2x + -3

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

Solving
-1x2 = -3 + -2x

Solving for variable 'x'.

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

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

Combine like terms: -3 + 3 = 0
3 + 2x + -1x2 = 0 + -2x + 2x
3 + 2x + -1x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
3 + 2x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {3, -1}

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