x(2x+3)(9)=810

Solution for x(2x+3)(9)=810 equation:

Simplifying
x(2x + 3)(9) = 810

Reorder the terms:
x(3 + 2x)(9) = 810

Reorder the terms for easier multiplication:
9x(3 + 2x) = 810
(3 * 9x + 2x * 9x) = 810
(27x + 18x2) = 810

Solving
27x + 18x2 = 810

Solving for variable 'x'.

Reorder the terms:
-810 + 27x + 18x2 = 810 + -810

Combine like terms: 810 + -810 = 0
-810 + 27x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-90 + 3x + 2x2) = 0

Factor a trinomial.
9((-15 + -2x)(6 + -1x)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7.5, 6}