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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
5 + -3x + -2x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
5 + -3x + -2x2 = 0 + x + -1x
5 + -3x + -2x2 = x + -1x

Combine like terms: x + -1x = 0
5 + -3x + -2x2 = 0

Factor a trinomial.
(1 + -1x)(5 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {1, -2.5}