-17x=x^2+72

Solution for -17x=x^2+72 equation:

Simplifying
-17x = x2 + 72

Reorder the terms:
-17x = 72 + x2

Solving
-17x = 72 + x2

Solving for variable 'x'.

Reorder the terms:
-72 + -17x + -1x2 = 72 + x2 + -72 + -1x2

Reorder the terms:
-72 + -17x + -1x2 = 72 + -72 + x2 + -1x2

Combine like terms: 72 + -72 = 0
-72 + -17x + -1x2 = 0 + x2 + -1x2
-72 + -17x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-72 + -17x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(72 + 17x + x2) = 0

Factor a trinomial.
-1((9 + x)(8 + x)) = 0

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

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-9, -8}