6x(x+15)=-42

Solution for 6x(x+15)=-42 equation:

Simplifying
6x(x + 15) = -42

Reorder the terms:
6x(15 + x) = -42
(15 * 6x + x * 6x) = -42
(90x + 6x2) = -42

Solving
90x + 6x2 = -42

Solving for variable 'x'.

Reorder the terms:
42 + 90x + 6x2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 90x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 15x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 15x + x2 = 0

Solving
7 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 15x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 15x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 15x + x2 = 0 + -7
15x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
15x + x2 = -7

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -7 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -7 + 56.25

Combine like terms: -7 + 56.25 = 49.25
56.25 + 15x + x2 = 49.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(x + 7.5) equal to 7.017834424 and -7.017834424.

Subproblem 1
x + 7.5 = 7.017834424

Simplifying
x + 7.5 = 7.017834424

Reorder the terms:
7.5 + x = 7.017834424

Solving
7.5 + x = 7.017834424

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 7.017834424 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 7.017834424 + -7.5
x = 7.017834424 + -7.5

Combine like terms: 7.017834424 + -7.5 = -0.482165576
x = -0.482165576

Simplifying
x = -0.482165576

Subproblem 2
x + 7.5 = -7.017834424

Simplifying
x + 7.5 = -7.017834424

Reorder the terms:
7.5 + x = -7.017834424

Solving
7.5 + x = -7.017834424

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -7.017834424 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -7.017834424 + -7.5
x = -7.017834424 + -7.5

Combine like terms: -7.017834424 + -7.5 = -14.517834424
x = -14.517834424

Simplifying
x = -14.517834424

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.482165576, -14.517834424}
Solution
x = {-0.482165576, -14.517834424}