(x+2)(x+3)+x=166

Solution for (x+2)(x+3)+x=166 equation:

Simplifying
(x + 2)(x + 3) + x = 166

Reorder the terms:
(2 + x)(x + 3) + x = 166

Reorder the terms:
(2 + x)(3 + x) + x = 166

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) + x = 166
((3 * 2 + x * 2) + x(3 + x)) + x = 166
((6 + 2x) + x(3 + x)) + x = 166
(6 + 2x + (3 * x + x * x)) + x = 166
(6 + 2x + (3x + x2)) + x = 166

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) + x = 166

Reorder the terms:
6 + 5x + x + x2 = 166

Combine like terms: 5x + x = 6x
6 + 6x + x2 = 166

Solving
6 + 6x + x2 = 166

Solving for variable 'x'.

Reorder the terms:
6 + -166 + 6x + x2 = 166 + -166

Combine like terms: 6 + -166 = -160
-160 + 6x + x2 = 166 + -166

Combine like terms: 166 + -166 = 0
-160 + 6x + x2 = 0

Factor a trinomial.
(-16 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-16, 10}