(x-15)(x+1)=17

Solution for (x-15)(x+1)=17 equation:

Simplifying
(x + -15)(x + 1) = 17

Reorder the terms:
(-15 + x)(x + 1) = 17

Reorder the terms:
(-15 + x)(1 + x) = 17

Multiply (-15 + x) * (1 + x)
(-15(1 + x) + x(1 + x)) = 17
((1 * -15 + x * -15) + x(1 + x)) = 17
((-15 + -15x) + x(1 + x)) = 17
(-15 + -15x + (1 * x + x * x)) = 17
(-15 + -15x + (1x + x2)) = 17

Combine like terms: -15x + 1x = -14x
(-15 + -14x + x2) = 17

Solving
-15 + -14x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
-15 + -17 + -14x + x2 = 17 + -17

Combine like terms: -15 + -17 = -32
-32 + -14x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-32 + -14x + x2 = 0

Factor a trinomial.
(-2 + -1x)(16 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-2, 16}