(x+5)(x)=66

Solution for (x+5)(x)=66 equation:

Simplifying
(x + 5)(x) = 66

Reorder the terms:
(5 + x)(x) = 66

Reorder the terms for easier multiplication:
x(5 + x) = 66
(5 * x + x * x) = 66
(5x + x2) = 66

Solving
5x + x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + 5x + x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 5x + x2 = 0

Factor a trinomial.
(-11 + -1x)(6 + -1x) = 0

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

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
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 = {-11, 6}