111=x^2+26x+24

Solution for 111=x^2+26x+24 equation:

Simplifying
111 = x2 + 26x + 24

Reorder the terms:
111 = 24 + 26x + x2

Solving
111 = 24 + 26x + x2

Solving for variable 'x'.

Combine like terms: 111 + -24 = 87
87 + -26x + -1x2 = 24 + 26x + x2 + -24 + -26x + -1x2

Reorder the terms:
87 + -26x + -1x2 = 24 + -24 + 26x + -26x + x2 + -1x2

Combine like terms: 24 + -24 = 0
87 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2
87 + -26x + -1x2 = 26x + -26x + x2 + -1x2

Combine like terms: 26x + -26x = 0
87 + -26x + -1x2 = 0 + x2 + -1x2
87 + -26x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
87 + -26x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(29 + x) = 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 '(29 + x)' equal to zero and attempt to solve:

Simplifying
29 + x = 0

Solving
29 + x = 0

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

Add '-29' to each side of the equation.
29 + -29 + x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + x = 0 + -29
x = 0 + -29

Combine like terms: 0 + -29 = -29
x = -29

Simplifying
x = -29
Solution
x = {3, -29}