=6(x^2+16.5x+10)

Solution for =6(x^2+16.5x+10) equation:

Simplifying
0 = 6(x2 + 16.5x + 10)

Reorder the terms:
0 = 6(10 + 16.5x + x2)
0 = (10 * 6 + 16.5x * 6 + x2 * 6)
0 = (60 + 99x + 6x2)

Solving
0 = 60 + 99x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -60 = -60
-60 + -99x + -6x2 = 60 + 99x + 6x2 + -60 + -99x + -6x2

Reorder the terms:
-60 + -99x + -6x2 = 60 + -60 + 99x + -99x + 6x2 + -6x2

Combine like terms: 60 + -60 = 0
-60 + -99x + -6x2 = 0 + 99x + -99x + 6x2 + -6x2
-60 + -99x + -6x2 = 99x + -99x + 6x2 + -6x2

Combine like terms: 99x + -99x = 0
-60 + -99x + -6x2 = 0 + 6x2 + -6x2
-60 + -99x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-60 + -99x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(20 + 33x + 2x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(20 + 33x + 2x2)' equal to zero and attempt to solve:

Simplifying
20 + 33x + 2x2 = 0

Solving
20 + 33x + 2x2 = 0

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

Divide each side by '2'.
10 + 16.5x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 16.5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 16.5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 16.5x + x2 = 0 + -10
16.5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
16.5x + x2 = -10

The x term is 16.5x.  Take half its coefficient (8.25).
Square it (68.0625) and add it to both sides.

Add '68.0625' to each side of the equation.
16.5x + 68.0625 + x2 = -10 + 68.0625

Reorder the terms:
68.0625 + 16.5x + x2 = -10 + 68.0625

Combine like terms: -10 + 68.0625 = 58.0625
68.0625 + 16.5x + x2 = 58.0625

Factor a perfect square on the left side:
(x + 8.25)(x + 8.25) = 58.0625

Calculate the square root of the right side: 7.619875327

Break this problem into two subproblems by setting 
(x + 8.25) equal to 7.619875327 and -7.619875327.

Subproblem 1
x + 8.25 = 7.619875327

Simplifying
x + 8.25 = 7.619875327

Reorder the terms:
8.25 + x = 7.619875327

Solving
8.25 + x = 7.619875327

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = 7.619875327 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = 7.619875327 + -8.25
x = 7.619875327 + -8.25

Combine like terms: 7.619875327 + -8.25 = -0.630124673
x = -0.630124673

Simplifying
x = -0.630124673

Subproblem 2
x + 8.25 = -7.619875327

Simplifying
x + 8.25 = -7.619875327

Reorder the terms:
8.25 + x = -7.619875327

Solving
8.25 + x = -7.619875327

Solving for variable 'x'.

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

Add '-8.25' to each side of the equation.
8.25 + -8.25 + x = -7.619875327 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + x = -7.619875327 + -8.25
x = -7.619875327 + -8.25

Combine like terms: -7.619875327 + -8.25 = -15.869875327
x = -15.869875327

Simplifying
x = -15.869875327

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.630124673, -15.869875327}
Solution
x = {-0.630124673, -15.869875327}