0=27x-18-10x^2

Solution for 0=27x-18-10x^2 equation:

Simplifying
0 = 27x + -18 + -10x2

Reorder the terms:
0 = -18 + 27x + -10x2

Solving
0 = -18 + 27x + -10x2

Solving for variable 'x'.

Combine like terms: 0 + 18 = 18
18 + -27x + 10x2 = -18 + 27x + -10x2 + 18 + -27x + 10x2

Reorder the terms:
18 + -27x + 10x2 = -18 + 18 + 27x + -27x + -10x2 + 10x2

Combine like terms: -18 + 18 = 0
18 + -27x + 10x2 = 0 + 27x + -27x + -10x2 + 10x2
18 + -27x + 10x2 = 27x + -27x + -10x2 + 10x2

Combine like terms: 27x + -27x = 0
18 + -27x + 10x2 = 0 + -10x2 + 10x2
18 + -27x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
18 + -27x + 10x2 = 0

Factor a trinomial.
(6 + -5x)(3 + -2x) = 0

Subproblem 1
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
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 = {1.2, 1.5}