2x(x+1)=2-x

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-2, 0.5}