x^2-19x=1802

Solution for x^2-19x=1802 equation:

Simplifying
x2 + -19x = 1802

Reorder the terms:
-19x + x2 = 1802

Solving
-19x + x2 = 1802

Solving for variable 'x'.

Reorder the terms:
-1802 + -19x + x2 = 1802 + -1802

Combine like terms: 1802 + -1802 = 0
-1802 + -19x + x2 = 0

Factor a trinomial.
(-34 + -1x)(53 + -1x) = 0

Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34
Subproblem 2
Set the factor '(53 + -1x)' equal to zero and attempt to solve:

Simplifying
53 + -1x = 0

Solving
53 + -1x = 0

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

Add '-53' to each side of the equation.
53 + -53 + -1x = 0 + -53

Combine like terms: 53 + -53 = 0
0 + -1x = 0 + -53
-1x = 0 + -53

Combine like terms: 0 + -53 = -53
-1x = -53

Divide each side by '-1'.
x = 53

Simplifying
x = 53
Solution
x = {-34, 53}