(5a+3)(2a-6)=10

Solution for (5a+3)(2a-6)=10 equation:

Simplifying
(5a + 3)(2a + -6) = 10

Reorder the terms:
(3 + 5a)(2a + -6) = 10

Reorder the terms:
(3 + 5a)(-6 + 2a) = 10

Multiply (3 + 5a) * (-6 + 2a)
(3(-6 + 2a) + 5a * (-6 + 2a)) = 10
((-6 * 3 + 2a * 3) + 5a * (-6 + 2a)) = 10
((-18 + 6a) + 5a * (-6 + 2a)) = 10
(-18 + 6a + (-6 * 5a + 2a * 5a)) = 10
(-18 + 6a + (-30a + 10a2)) = 10

Combine like terms: 6a + -30a = -24a
(-18 + -24a + 10a2) = 10

Solving
-18 + -24a + 10a2 = 10

Solving for variable 'a'.

Reorder the terms:
-18 + -10 + -24a + 10a2 = 10 + -10

Combine like terms: -18 + -10 = -28
-28 + -24a + 10a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-28 + -24a + 10a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -12a + 5a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -12a + 5a2)' equal to zero and attempt to solve:

Simplifying
-14 + -12a + 5a2 = 0

Solving
-14 + -12a + 5a2 = 0

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

Divide each side by '5'.
-2.8 + -2.4a + a2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + -2.4a + 2.8 + a2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + -2.4a + a2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + -2.4a + a2 = 0 + 2.8
-2.4a + a2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
-2.4a + a2 = 2.8

The a term is -2.4a.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4a + 1.44 + a2 = 2.8 + 1.44

Reorder the terms:
1.44 + -2.4a + a2 = 2.8 + 1.44

Combine like terms: 2.8 + 1.44 = 4.24
1.44 + -2.4a + a2 = 4.24

Factor a perfect square on the left side:
(a + -1.2)(a + -1.2) = 4.24

Calculate the square root of the right side: 2.059126028

Break this problem into two subproblems by setting 
(a + -1.2) equal to 2.059126028 and -2.059126028.

Subproblem 1
a + -1.2 = 2.059126028

Simplifying
a + -1.2 = 2.059126028

Reorder the terms:
-1.2 + a = 2.059126028

Solving
-1.2 + a = 2.059126028

Solving for variable 'a'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + a = 2.059126028 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + a = 2.059126028 + 1.2
a = 2.059126028 + 1.2

Combine like terms: 2.059126028 + 1.2 = 3.259126028
a = 3.259126028

Simplifying
a = 3.259126028

Subproblem 2
a + -1.2 = -2.059126028

Simplifying
a + -1.2 = -2.059126028

Reorder the terms:
-1.2 + a = -2.059126028

Solving
-1.2 + a = -2.059126028

Solving for variable 'a'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + a = -2.059126028 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + a = -2.059126028 + 1.2
a = -2.059126028 + 1.2

Combine like terms: -2.059126028 + 1.2 = -0.859126028
a = -0.859126028

Simplifying
a = -0.859126028

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.259126028, -0.859126028}
Solution
a = {3.259126028, -0.859126028}