19x=x^2-42

Solution for 19x=x^2-42 equation:

Simplifying
19x = x2 + -42

Reorder the terms:
19x = -42 + x2

Solving
19x = -42 + x2

Solving for variable 'x'.

Reorder the terms:
42 + 19x + -1x2 = -42 + x2 + 42 + -1x2

Reorder the terms:
42 + 19x + -1x2 = -42 + 42 + x2 + -1x2

Combine like terms: -42 + 42 = 0
42 + 19x + -1x2 = 0 + x2 + -1x2
42 + 19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 19x + -1x2 = 0

Factor a trinomial.
(21 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {21, -2}