2x^2+9x-3=-x^2+x

Solution for 2x^2+9x-3=-x^2+x equation:

Simplifying
2x2 + 9x + -3 = -1x2 + x

Reorder the terms:
-3 + 9x + 2x2 = -1x2 + x

Reorder the terms:
-3 + 9x + 2x2 = x + -1x2

Solving
-3 + 9x + 2x2 = x + -1x2

Solving for variable 'x'.

Reorder the terms:
-3 + 9x + -1x + 2x2 + x2 = x + -1x2 + -1x + x2

Combine like terms: 9x + -1x = 8x
-3 + 8x + 2x2 + x2 = x + -1x2 + -1x + x2

Combine like terms: 2x2 + x2 = 3x2
-3 + 8x + 3x2 = x + -1x2 + -1x + x2

Reorder the terms:
-3 + 8x + 3x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-3 + 8x + 3x2 = 0 + -1x2 + x2
-3 + 8x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-3 + 8x + 3x2 = 0

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

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-3, 0.3333333333}