5x(12+x)=-13

Solution for 5x(12+x)=-13 equation:

Simplifying
5x(12 + x) = -13
(12 * 5x + x * 5x) = -13
(60x + 5x2) = -13

Solving
60x + 5x2 = -13

Solving for variable 'x'.

Reorder the terms:
13 + 60x + 5x2 = -13 + 13

Combine like terms: -13 + 13 = 0
13 + 60x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.6 + 12x + x2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + 12x + -2.6 + x2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + 12x + x2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + 12x + x2 = 0 + -2.6
12x + x2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
12x + x2 = -2.6

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -2.6 + 36

Reorder the terms:
36 + 12x + x2 = -2.6 + 36

Combine like terms: -2.6 + 36 = 33.4
36 + 12x + x2 = 33.4

Factor a perfect square on the left side:
(x + 6)(x + 6) = 33.4

Calculate the square root of the right side: 5.779273311

Break this problem into two subproblems by setting 
(x + 6) equal to 5.779273311 and -5.779273311.

Subproblem 1
x + 6 = 5.779273311

Simplifying
x + 6 = 5.779273311

Reorder the terms:
6 + x = 5.779273311

Solving
6 + x = 5.779273311

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 5.779273311 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.779273311 + -6
x = 5.779273311 + -6

Combine like terms: 5.779273311 + -6 = -0.220726689
x = -0.220726689

Simplifying
x = -0.220726689

Subproblem 2
x + 6 = -5.779273311

Simplifying
x + 6 = -5.779273311

Reorder the terms:
6 + x = -5.779273311

Solving
6 + x = -5.779273311

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -5.779273311 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.779273311 + -6
x = -5.779273311 + -6

Combine like terms: -5.779273311 + -6 = -11.779273311
x = -11.779273311

Simplifying
x = -11.779273311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.220726689, -11.779273311}