x(x-19)=120

Solution for x(x-19)=120 equation:

Simplifying
x(x + -19) = 120

Reorder the terms:
x(-19 + x) = 120
(-19 * x + x * x) = 120
(-19x + x2) = 120

Solving
-19x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + -19x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + -19x + x2 = 0

Factor a trinomial.
(-5 + -1x)(24 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(24 + -1x)' equal to zero and attempt to solve:

Simplifying
24 + -1x = 0

Solving
24 + -1x = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1x = 0 + -24
-1x = 0 + -24

Combine like terms: 0 + -24 = -24
-1x = -24

Divide each side by '-1'.
x = 24

Simplifying
x = 24
Solution
x = {-5, 24}