x^2=19x+42

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

Simplifying
x2 = 19x + 42

Reorder the terms:
x2 = 42 + 19x

Solving
x2 = 42 + 19x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(-2 + -1x)(21 + -1x) = 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 + -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
Solution
x = {-2, 21}