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

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

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

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

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

Add '-2x' to each side of the equation.
6 + 2x + -2x + -1x2 = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 0 + -1x2 = -3 + 2x + -2x
6 + -1x2 = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -1x2 = -3 + 0
6 + -1x2 = -3

Solving
6 + -1x2 = -3

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = -3 + -6

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

Combine like terms: -3 + -6 = -9
-1x2 = -9

Divide each side by '-1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}