x(x+6)11=297

Solution for x(x+6)11=297 equation:

Simplifying
x(x + 6) * 11 = 297

Reorder the terms:
x(6 + x) * 11 = 297

Reorder the terms for easier multiplication:
11x(6 + x) = 297
(6 * 11x + x * 11x) = 297
(66x + 11x2) = 297

Solving
66x + 11x2 = 297

Solving for variable 'x'.

Reorder the terms:
-297 + 66x + 11x2 = 297 + -297

Combine like terms: 297 + -297 = 0
-297 + 66x + 11x2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(-27 + 6x + x2) = 0

Factor a trinomial.
11((-9 + -1x)(3 + -1x)) = 0

Ignore the factor 11.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
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 = {-9, 3}