18x^2-63x+45=0

Solution for 18x^2-63x+45=0 equation:

Simplifying
18x2 + -63x + 45 = 0

Reorder the terms:
45 + -63x + 18x2 = 0

Solving
45 + -63x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(5 + -7x + 2x2) = 0

Factor a trinomial.
9((1 + -1x)(5 + -2x)) = 0

Ignore the factor 9.
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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}