0=-x^2+17x-42

Solution for 0=-x^2+17x-42 equation:

Simplifying
0 = -1x2 + 17x + -42

Reorder the terms:
0 = -42 + 17x + -1x2

Solving
0 = -42 + 17x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + -17x + x2 = -42 + 17x + -1x2 + 42 + -17x + x2

Reorder the terms:
42 + -17x + x2 = -42 + 42 + 17x + -17x + -1x2 + x2

Combine like terms: -42 + 42 = 0
42 + -17x + x2 = 0 + 17x + -17x + -1x2 + x2
42 + -17x + x2 = 17x + -17x + -1x2 + x2

Combine like terms: 17x + -17x = 0
42 + -17x + x2 = 0 + -1x2 + x2
42 + -17x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
42 + -17x + x2 = 0

Factor a trinomial.
(3 + -1x)(14 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {3, 14}