(x-51)(x+17)=0

Solution for (x-51)(x+17)=0 equation:

Simplifying
(x + -51)(x + 17) = 0

Reorder the terms:
(-51 + x)(x + 17) = 0

Reorder the terms:
(-51 + x)(17 + x) = 0

Multiply (-51 + x) * (17 + x)
(-51(17 + x) + x(17 + x)) = 0
((17 * -51 + x * -51) + x(17 + x)) = 0
((-867 + -51x) + x(17 + x)) = 0
(-867 + -51x + (17 * x + x * x)) = 0
(-867 + -51x + (17x + x2)) = 0

Combine like terms: -51x + 17x = -34x
(-867 + -34x + x2) = 0

Solving
-867 + -34x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -1x)(51 + -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 '(51 + -1x)' equal to zero and attempt to solve:

Simplifying
51 + -1x = 0

Solving
51 + -1x = 0

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

Add '-51' to each side of the equation.
51 + -51 + -1x = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -1x = 0 + -51
-1x = 0 + -51

Combine like terms: 0 + -51 = -51
-1x = -51

Divide each side by '-1'.
x = 51

Simplifying
x = 51
Solution
x = {-17, 51}