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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

Combine like terms: 1 + -1 = 0
-1 + 3x + 4x2 = 0 + -2x2 + 2x2
-1 + 3x + 4x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-1 + 3x + 4x2 = 0

Factor a trinomial.
(-1 + -1x)(1 + -4x) = 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 '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-1, 0.25}