(10+x)(5+x)=176

Solution for (10+x)(5+x)=176 equation:

Simplifying
(10 + x)(5 + x) = 176

Multiply (10 + x) * (5 + x)
(10(5 + x) + x(5 + x)) = 176
((5 * 10 + x * 10) + x(5 + x)) = 176
((50 + 10x) + x(5 + x)) = 176
(50 + 10x + (5 * x + x * x)) = 176
(50 + 10x + (5x + x2)) = 176

Combine like terms: 10x + 5x = 15x
(50 + 15x + x2) = 176

Solving
50 + 15x + x2 = 176

Solving for variable 'x'.

Reorder the terms:
50 + -176 + 15x + x2 = 176 + -176

Combine like terms: 50 + -176 = -126
-126 + 15x + x2 = 176 + -176

Combine like terms: 176 + -176 = 0
-126 + 15x + x2 = 0

Factor a trinomial.
(-21 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = 0 + 21
-1x = 0 + 21

Combine like terms: 0 + 21 = 21
-1x = 21

Divide each side by '-1'.
x = -21

Simplifying
x = -21
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 = {-21, 6}