2x^2=9x-9

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

Simplifying
2x2 = 9x + -9

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

Solving
2x2 = -9 + 9x

Solving for variable 'x'.

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

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

Combine like terms: -9 + 9 = 0
9 + -9x + 2x2 = 0 + 9x + -9x
9 + -9x + 2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
9 + -9x + 2x2 = 0

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

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

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
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
Solution
x = {1.5, 3}