42=19x+x^2

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

Simplifying
42 = 19x + x2

Solving
42 = 19x + x2

Solving for variable 'x'.

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

Combine like terms: 19x + -19x = 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.
(2 + -1x)(21 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

Simplifying
21 + x = 0

Solving
21 + x = 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 + x = 0 + -21

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

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

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