9x^2=18x+27

Solution for 9x^2=18x+27 equation:

Simplifying
9x2 = 18x + 27

Reorder the terms:
9x2 = 27 + 18x

Solving
9x2 = 27 + 18x

Solving for variable 'x'.

Reorder the terms:
-27 + -18x + 9x2 = 27 + 18x + -27 + -18x

Reorder the terms:
-27 + -18x + 9x2 = 27 + -27 + 18x + -18x

Combine like terms: 27 + -27 = 0
-27 + -18x + 9x2 = 0 + 18x + -18x
-27 + -18x + 9x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-27 + -18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + -2x + x2) = 0

Factor a trinomial.
9((-1 + -1x)(3 + -1x)) = 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 '(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, 3}