-3x^2=x-2

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

Simplifying
-3x2 = x + -2

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

Solving
-3x2 = -2 + x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(2 + -3x)(1 + x) = 0

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0.6666666667, -1}