(5+x)(10+x)=126

Solution for (5+x)(10+x)=126 equation:

Simplifying
(5 + x)(10 + x) = 126

Multiply (5 + x) * (10 + x)
(5(10 + x) + x(10 + x)) = 126
((10 * 5 + x * 5) + x(10 + x)) = 126
((50 + 5x) + x(10 + x)) = 126
(50 + 5x + (10 * x + x * x)) = 126
(50 + 5x + (10x + x2)) = 126

Combine like terms: 5x + 10x = 15x
(50 + 15x + x2) = 126

Solving
50 + 15x + x2 = 126

Solving for variable 'x'.

Reorder the terms:
50 + -126 + 15x + x2 = 126 + -126

Combine like terms: 50 + -126 = -76
-76 + 15x + x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-76 + 15x + x2 = 0

Factor a trinomial.
(-19 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-19, 4}