3(5a^2-1)=6(a+2)

Solution for 3(5a^2-1)=6(a+2) equation:

Simplifying
3(5a2 + -1) = 6(a + 2)

Reorder the terms:
3(-1 + 5a2) = 6(a + 2)
(-1 * 3 + 5a2 * 3) = 6(a + 2)
(-3 + 15a2) = 6(a + 2)

Reorder the terms:
-3 + 15a2 = 6(2 + a)
-3 + 15a2 = (2 * 6 + a * 6)
-3 + 15a2 = (12 + 6a)

Solving
-3 + 15a2 = 12 + 6a

Solving for variable 'a'.

Reorder the terms:
-3 + -12 + -6a + 15a2 = 12 + 6a + -12 + -6a

Combine like terms: -3 + -12 = -15
-15 + -6a + 15a2 = 12 + 6a + -12 + -6a

Reorder the terms:
-15 + -6a + 15a2 = 12 + -12 + 6a + -6a

Combine like terms: 12 + -12 = 0
-15 + -6a + 15a2 = 0 + 6a + -6a
-15 + -6a + 15a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
-15 + -6a + 15a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -2a + 5a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2a + 5a2)' equal to zero and attempt to solve:

Simplifying
-5 + -2a + 5a2 = 0

Solving
-5 + -2a + 5a2 = 0

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

Divide each side by '5'.
-1 + -0.4a + a2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.4a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.4a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.4a + a2 = 0 + 1
-0.4a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.4a + a2 = 1

The a term is -0.4a.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4a + 0.04 + a2 = 1 + 0.04

Reorder the terms:
0.04 + -0.4a + a2 = 1 + 0.04

Combine like terms: 1 + 0.04 = 1.04
0.04 + -0.4a + a2 = 1.04

Factor a perfect square on the left side:
(a + -0.2)(a + -0.2) = 1.04

Calculate the square root of the right side: 1.019803903

Break this problem into two subproblems by setting 
(a + -0.2) equal to 1.019803903 and -1.019803903.

Subproblem 1
a + -0.2 = 1.019803903

Simplifying
a + -0.2 = 1.019803903

Reorder the terms:
-0.2 + a = 1.019803903

Solving
-0.2 + a = 1.019803903

Solving for variable 'a'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + a = 1.019803903 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + a = 1.019803903 + 0.2
a = 1.019803903 + 0.2

Combine like terms: 1.019803903 + 0.2 = 1.219803903
a = 1.219803903

Simplifying
a = 1.219803903

Subproblem 2
a + -0.2 = -1.019803903

Simplifying
a + -0.2 = -1.019803903

Reorder the terms:
-0.2 + a = -1.019803903

Solving
-0.2 + a = -1.019803903

Solving for variable 'a'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + a = -1.019803903 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + a = -1.019803903 + 0.2
a = -1.019803903 + 0.2

Combine like terms: -1.019803903 + 0.2 = -0.819803903
a = -0.819803903

Simplifying
a = -0.819803903

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.219803903, -0.819803903}
Solution
a = {1.219803903, -0.819803903}