11x=x^2-42

Solution for 11x=x^2-42 equation:

Simplifying
11x = x2 + -42

Reorder the terms:
11x = -42 + x2

Solving
11x = -42 + x2

Solving for variable 'x'.

Reorder the terms:
42 + 11x + -1x2 = -42 + x2 + 42 + -1x2

Reorder the terms:
42 + 11x + -1x2 = -42 + 42 + x2 + -1x2

Combine like terms: -42 + 42 = 0
42 + 11x + -1x2 = 0 + x2 + -1x2
42 + 11x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 11x + -1x2 = 0

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

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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