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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: -2x + -3x = -5x
6 + -5x + -1x2 = -3 + 3x + x2 + 3 + -3x + -1x2

Reorder the terms:
6 + -5x + -1x2 = -3 + 3 + 3x + -3x + x2 + -1x2

Combine like terms: -3 + 3 = 0
6 + -5x + -1x2 = 0 + 3x + -3x + x2 + -1x2
6 + -5x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
6 + -5x + -1x2 = 0 + x2 + -1x2
6 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
6 + -5x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {1, -6}