(10+x)(8+x)=120

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Solution for (10+x)(8+x)=120 equation: 


Simplifying
(10 + x)(8 + x) = 120

Multiply (10 + x) * (8 + x)
(10(8 + x) + x(8 + x)) = 120
((8 * 10 + x * 10) + x(8 + x)) = 120
((80 + 10x) + x(8 + x)) = 120
(80 + 10x + (8 * x + x * x)) = 120
(80 + 10x + (8x + x2)) = 120

Combine like terms: 10x + 8x = 18x
(80 + 18x + x2) = 120

Solving
80 + 18x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
80 + -120 + 18x + x2 = 120 + -120

Combine like terms: 80 + -120 = -40
-40 + 18x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-40 + 18x + x2 = 0

Factor a trinomial.
(-20 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-20, 2}

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