(x+17)(x-22)=0

Solution for (x+17)(x-22)=0 equation:

Simplifying
(x + 17)(x + -22) = 0

Reorder the terms:
(17 + x)(x + -22) = 0

Reorder the terms:
(17 + x)(-22 + x) = 0

Multiply (17 + x) * (-22 + x)
(17(-22 + x) + x(-22 + x)) = 0
((-22 * 17 + x * 17) + x(-22 + x)) = 0
((-374 + 17x) + x(-22 + x)) = 0
(-374 + 17x + (-22 * x + x * x)) = 0
(-374 + 17x + (-22x + x2)) = 0

Combine like terms: 17x + -22x = -5x
(-374 + -5x + x2) = 0

Solving
-374 + -5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -1x)(22 + -1x) = 0

Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-17, 22}