-3a(a+14)=6(2a+3)

Solution for -3a(a+14)=6(2a+3) equation:

Simplifying
-3a(a + 14) = 6(2a + 3)

Reorder the terms:
-3a(14 + a) = 6(2a + 3)
(14 * -3a + a * -3a) = 6(2a + 3)
(-42a + -3a2) = 6(2a + 3)

Reorder the terms:
-42a + -3a2 = 6(3 + 2a)
-42a + -3a2 = (3 * 6 + 2a * 6)
-42a + -3a2 = (18 + 12a)

Solving
-42a + -3a2 = 18 + 12a

Solving for variable 'a'.

Reorder the terms:
-18 + -42a + -12a + -3a2 = 18 + 12a + -18 + -12a

Combine like terms: -42a + -12a = -54a
-18 + -54a + -3a2 = 18 + 12a + -18 + -12a

Reorder the terms:
-18 + -54a + -3a2 = 18 + -18 + 12a + -12a

Combine like terms: 18 + -18 = 0
-18 + -54a + -3a2 = 0 + 12a + -12a
-18 + -54a + -3a2 = 12a + -12a

Combine like terms: 12a + -12a = 0
-18 + -54a + -3a2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6 + 18a + a2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(6 + 18a + a2)' equal to zero and attempt to solve:

Simplifying
6 + 18a + a2 = 0

Solving
6 + 18a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 18a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + 18a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 18a + a2 = 0 + -6
18a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
18a + a2 = -6

The a term is 18a.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18a + 81 + a2 = -6 + 81

Reorder the terms:
81 + 18a + a2 = -6 + 81

Combine like terms: -6 + 81 = 75
81 + 18a + a2 = 75

Factor a perfect square on the left side:
(a + 9)(a + 9) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(a + 9) equal to 8.660254038 and -8.660254038.

Subproblem 1
a + 9 = 8.660254038

Simplifying
a + 9 = 8.660254038

Reorder the terms:
9 + a = 8.660254038

Solving
9 + a = 8.660254038

Solving for variable 'a'.

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

Add '-9' to each side of the equation.
9 + -9 + a = 8.660254038 + -9

Combine like terms: 9 + -9 = 0
0 + a = 8.660254038 + -9
a = 8.660254038 + -9

Combine like terms: 8.660254038 + -9 = -0.339745962
a = -0.339745962

Simplifying
a = -0.339745962

Subproblem 2
a + 9 = -8.660254038

Simplifying
a + 9 = -8.660254038

Reorder the terms:
9 + a = -8.660254038

Solving
9 + a = -8.660254038

Solving for variable 'a'.

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

Add '-9' to each side of the equation.
9 + -9 + a = -8.660254038 + -9

Combine like terms: 9 + -9 = 0
0 + a = -8.660254038 + -9
a = -8.660254038 + -9

Combine like terms: -8.660254038 + -9 = -17.660254038
a = -17.660254038

Simplifying
a = -17.660254038

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.339745962, -17.660254038}
Solution
a = {-0.339745962, -17.660254038}