0=-x^2+28(x)-171

Solution for 0=-x^2+28(x)-171 equation:

Simplifying
0 = -1x2 + 28(x) + -171

Reorder the terms:
0 = -171 + 28x + -1x2

Solving
0 = -171 + 28x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 171 = 171
171 + -28x + x2 = -171 + 28x + -1x2 + 171 + -28x + x2

Reorder the terms:
171 + -28x + x2 = -171 + 171 + 28x + -28x + -1x2 + x2

Combine like terms: -171 + 171 = 0
171 + -28x + x2 = 0 + 28x + -28x + -1x2 + x2
171 + -28x + x2 = 28x + -28x + -1x2 + x2

Combine like terms: 28x + -28x = 0
171 + -28x + x2 = 0 + -1x2 + x2
171 + -28x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
171 + -28x + x2 = 0

Factor a trinomial.
(9 + -1x)(19 + -1x) = 0

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
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 = {9, 19}