0=2x^2-9x+9

Solution for 0=2x^2-9x+9 equation:

Simplifying
0 = 2x2 + -9x + 9

Reorder the terms:
0 = 9 + -9x + 2x2

Solving
0 = 9 + -9x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
-3 + x = 0

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

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

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

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