-6a-15=-3a(a-7)

Solution for -6a-15=-3a(a-7) equation:

Simplifying
-6a + -15 = -3a(a + -7)

Reorder the terms:
-15 + -6a = -3a(a + -7)

Reorder the terms:
-15 + -6a = -3a(-7 + a)
-15 + -6a = (-7 * -3a + a * -3a)
-15 + -6a = (21a + -3a2)

Solving
-15 + -6a = 21a + -3a2

Solving for variable 'a'.

Combine like terms: -6a + -21a = -27a
-15 + -27a + 3a2 = 21a + -3a2 + -21a + 3a2

Reorder the terms:
-15 + -27a + 3a2 = 21a + -21a + -3a2 + 3a2

Combine like terms: 21a + -21a = 0
-15 + -27a + 3a2 = 0 + -3a2 + 3a2
-15 + -27a + 3a2 = -3a2 + 3a2

Combine like terms: -3a2 + 3a2 = 0
-15 + -27a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -9a + a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -9a + a2)' equal to zero and attempt to solve:

Simplifying
-5 + -9a + a2 = 0

Solving
-5 + -9a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -9a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + -9a + a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -9a + a2 = 0 + 5
-9a + a2 = 0 + 5

Combine like terms: 0 + 5 = 5
-9a + a2 = 5

The a term is -9a.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9a + 20.25 + a2 = 5 + 20.25

Reorder the terms:
20.25 + -9a + a2 = 5 + 20.25

Combine like terms: 5 + 20.25 = 25.25
20.25 + -9a + a2 = 25.25

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(a + -4.5) equal to 5.024937811 and -5.024937811.

Subproblem 1
a + -4.5 = 5.024937811

Simplifying
a + -4.5 = 5.024937811

Reorder the terms:
-4.5 + a = 5.024937811

Solving
-4.5 + a = 5.024937811

Solving for variable 'a'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + a = 5.024937811 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + a = 5.024937811 + 4.5
a = 5.024937811 + 4.5

Combine like terms: 5.024937811 + 4.5 = 9.524937811
a = 9.524937811

Simplifying
a = 9.524937811

Subproblem 2
a + -4.5 = -5.024937811

Simplifying
a + -4.5 = -5.024937811

Reorder the terms:
-4.5 + a = -5.024937811

Solving
-4.5 + a = -5.024937811

Solving for variable 'a'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + a = -5.024937811 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + a = -5.024937811 + 4.5
a = -5.024937811 + 4.5

Combine like terms: -5.024937811 + 4.5 = -0.524937811
a = -0.524937811

Simplifying
a = -0.524937811

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {9.524937811, -0.524937811}
Solution
a = {9.524937811, -0.524937811}