2x-5=-2x^2-1

Solution for 2x-5=-2x^2-1 equation:

Simplifying
2x + -5 = -2x2 + -1

Reorder the terms:
-5 + 2x = -2x2 + -1

Reorder the terms:
-5 + 2x = -1 + -2x2

Solving
-5 + 2x = -1 + -2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 1 + 2x + 2x2 = -1 + -2x2 + 1 + 2x2

Combine like terms: -5 + 1 = -4
-4 + 2x + 2x2 = -1 + -2x2 + 1 + 2x2

Reorder the terms:
-4 + 2x + 2x2 = -1 + 1 + -2x2 + 2x2

Combine like terms: -1 + 1 = 0
-4 + 2x + 2x2 = 0 + -2x2 + 2x2
-4 + 2x + 2x2 = -2x2 + 2x2

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

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

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

Ignore the factor 2.
Subproblem 1
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
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}