=27x^2-90x+27

Solution for =27x^2-90x+27 equation:

Simplifying
0 = 27x2 + -90x + 27

Reorder the terms:
0 = 27 + -90x + 27x2

Solving
0 = 27 + -90x + 27x2

Solving for variable 'x'.

Combine like terms: 0 + -27 = -27
-27 + 90x + -27x2 = 27 + -90x + 27x2 + -27 + 90x + -27x2

Reorder the terms:
-27 + 90x + -27x2 = 27 + -27 + -90x + 90x + 27x2 + -27x2

Combine like terms: 27 + -27 = 0
-27 + 90x + -27x2 = 0 + -90x + 90x + 27x2 + -27x2
-27 + 90x + -27x2 = -90x + 90x + 27x2 + -27x2

Combine like terms: -90x + 90x = 0
-27 + 90x + -27x2 = 0 + 27x2 + -27x2
-27 + 90x + -27x2 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
-27 + 90x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + 10x + -3x2) = 0

Factor a trinomial.
9((-3 + x)(1 + -3x)) = 0

Ignore the factor 9.
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 '(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}