10a+5a(a-3)=15

Solution for 10a+5a(a-3)=15 equation:

Simplifying
10a + 5a(a + -3) = 15

Reorder the terms:
10a + 5a(-3 + a) = 15
10a + (-3 * 5a + a * 5a) = 15
10a + (-15a + 5a2) = 15

Combine like terms: 10a + -15a = -5a
-5a + 5a2 = 15

Solving
-5a + 5a2 = 15

Solving for variable 'a'.

Reorder the terms:
-15 + -5a + 5a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -5a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -1a + a2) = 0

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

Simplifying
-3 + -1a + a2 = 0

Solving
-3 + -1a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + -1a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a + a2 = 0 + 3
-1a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1a + a2 = 3

The a term is -1a.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1a + 0.25 + a2 = 3 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1a + a2 = 3.25

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(a + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
a + -0.5 = 1.802775638

Simplifying
a + -0.5 = 1.802775638

Reorder the terms:
-0.5 + a = 1.802775638

Solving
-0.5 + a = 1.802775638

Solving for variable 'a'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + a = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = 1.802775638 + 0.5
a = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
a = 2.302775638

Simplifying
a = 2.302775638

Subproblem 2
a + -0.5 = -1.802775638

Simplifying
a + -0.5 = -1.802775638

Reorder the terms:
-0.5 + a = -1.802775638

Solving
-0.5 + a = -1.802775638

Solving for variable 'a'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + a = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = -1.802775638 + 0.5
a = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
a = -1.302775638

Simplifying
a = -1.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.302775638, -1.302775638}
Solution
a = {2.302775638, -1.302775638}