(15-x)(x+5)=96

Solution for (15-x)(x+5)=96 equation:

Simplifying
(15 + -1x)(x + 5) = 96

Reorder the terms:
(15 + -1x)(5 + x) = 96

Multiply (15 + -1x) * (5 + x)
(15(5 + x) + -1x * (5 + x)) = 96
((5 * 15 + x * 15) + -1x * (5 + x)) = 96
((75 + 15x) + -1x * (5 + x)) = 96
(75 + 15x + (5 * -1x + x * -1x)) = 96
(75 + 15x + (-5x + -1x2)) = 96

Combine like terms: 15x + -5x = 10x
(75 + 10x + -1x2) = 96

Solving
75 + 10x + -1x2 = 96

Solving for variable 'x'.

Reorder the terms:
75 + -96 + 10x + -1x2 = 96 + -96

Combine like terms: 75 + -96 = -21
-21 + 10x + -1x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-21 + 10x + -1x2 = 0

Factor a trinomial.
(-7 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {7, 3}