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

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

Simplifying
x2 + x = 3(1 + -1x2)

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

Solving
x + x2 = 3 + -3x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-1 + -1x)(3 + -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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1, 0.75}