-x^2+2x+58=-x+4

Solution for -x^2+2x+58=-x+4 equation:

Simplifying
-1x2 + 2x + 58 = -1x + 4

Reorder the terms:
58 + 2x + -1x2 = -1x + 4

Reorder the terms:
58 + 2x + -1x2 = 4 + -1x

Solving
58 + 2x + -1x2 = 4 + -1x

Solving for variable 'x'.

Reorder the terms:
58 + -4 + 2x + x + -1x2 = 4 + -1x + -4 + x

Combine like terms: 58 + -4 = 54
54 + 2x + x + -1x2 = 4 + -1x + -4 + x

Combine like terms: 2x + x = 3x
54 + 3x + -1x2 = 4 + -1x + -4 + x

Reorder the terms:
54 + 3x + -1x2 = 4 + -4 + -1x + x

Combine like terms: 4 + -4 = 0
54 + 3x + -1x2 = 0 + -1x + x
54 + 3x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
54 + 3x + -1x2 = 0

Factor a trinomial.
(9 + -1x)(6 + x) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {9, -6}