x(x+19)=-84

Solution for x(x+19)=-84 equation:

Simplifying
x(x + 19) = -84

Reorder the terms:
x(19 + x) = -84
(19 * x + x * x) = -84
(19x + x2) = -84

Solving
19x + x2 = -84

Solving for variable 'x'.

Reorder the terms:
84 + 19x + x2 = -84 + 84

Combine like terms: -84 + 84 = 0
84 + 19x + x2 = 0

Factor a trinomial.
(12 + x)(7 + x) = 0

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {-12, -7}