(x-19)(x+17)=

Solution for (x-19)(x+17)= equation:

Simplifying
(x + -19)(x + 17) = 0

Reorder the terms:
(-19 + x)(x + 17) = 0

Reorder the terms:
(-19 + x)(17 + x) = 0

Multiply (-19 + x) * (17 + x)
(-19(17 + x) + x(17 + x)) = 0
((17 * -19 + x * -19) + x(17 + x)) = 0
((-323 + -19x) + x(17 + x)) = 0
(-323 + -19x + (17 * x + x * x)) = 0
(-323 + -19x + (17x + x2)) = 0

Combine like terms: -19x + 17x = -2x
(-323 + -2x + x2) = 0

Solving
-323 + -2x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -1x)(19 + -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 '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-17, 19}