-x^2+3=(2x-1)2

Solution for -x^2+3=(2x-1)2 equation:

Simplifying
-1x2 + 3 = (2x + -1) * 2

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

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

Reorder the terms for easier multiplication:
3 + -1x2 = 2(-1 + 2x)
3 + -1x2 = (-1 * 2 + 2x * 2)
3 + -1x2 = (-2 + 4x)

Solving
3 + -1x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
3 + 2 + -4x + -1x2 = -2 + 4x + 2 + -4x

Combine like terms: 3 + 2 = 5
5 + -4x + -1x2 = -2 + 4x + 2 + -4x

Reorder the terms:
5 + -4x + -1x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
5 + -4x + -1x2 = 0 + 4x + -4x
5 + -4x + -1x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
5 + -4x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(5 + x) = 0

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {1, -5}