(6+x)(4+x)=80

Solution for (6+x)(4+x)=80 equation:

Simplifying
(6 + x)(4 + x) = 80

Multiply (6 + x) * (4 + x)
(6(4 + x) + x(4 + x)) = 80
((4 * 6 + x * 6) + x(4 + x)) = 80
((24 + 6x) + x(4 + x)) = 80
(24 + 6x + (4 * x + x * x)) = 80
(24 + 6x + (4x + x2)) = 80

Combine like terms: 6x + 4x = 10x
(24 + 10x + x2) = 80

Solving
24 + 10x + x2 = 80

Solving for variable 'x'.

Reorder the terms:
24 + -80 + 10x + x2 = 80 + -80

Combine like terms: 24 + -80 = -56
-56 + 10x + x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-56 + 10x + x2 = 0

Factor a trinomial.
(-14 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
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 = {-14, 4}