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

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

Simplifying
2(3a + -5) * 2 + -1(a + 1)(a + -1) = 0

Reorder the terms:
2(-5 + 3a) * 2 + -1(a + 1)(a + -1) = 0

Reorder the terms for easier multiplication:
2 * 2(-5 + 3a) + -1(a + 1)(a + -1) = 0

Multiply 2 * 2
4(-5 + 3a) + -1(a + 1)(a + -1) = 0
(-5 * 4 + 3a * 4) + -1(a + 1)(a + -1) = 0
(-20 + 12a) + -1(a + 1)(a + -1) = 0

Reorder the terms:
-20 + 12a + -1(1 + a)(a + -1) = 0

Reorder the terms:
-20 + 12a + -1(1 + a)(-1 + a) = 0

Multiply (1 + a) * (-1 + a)
-20 + 12a + -1(1(-1 + a) + a(-1 + a)) = 0
-20 + 12a + -1((-1 * 1 + a * 1) + a(-1 + a)) = 0
-20 + 12a + -1((-1 + 1a) + a(-1 + a)) = 0
-20 + 12a + -1(-1 + 1a + (-1 * a + a * a)) = 0
-20 + 12a + -1(-1 + 1a + (-1a + a2)) = 0

Combine like terms: 1a + -1a = 0
-20 + 12a + -1(-1 + 0 + a2) = 0
-20 + 12a + -1(-1 + a2) = 0
-20 + 12a + (-1 * -1 + a2 * -1) = 0
-20 + 12a + (1 + -1a2) = 0

Reorder the terms:
-20 + 1 + 12a + -1a2 = 0

Combine like terms: -20 + 1 = -19
-19 + 12a + -1a2 = 0

Solving
-19 + 12a + -1a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
19 + -12a + a2 = 0

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -12a + -19 + a2 = 0 + -19

Reorder the terms:
19 + -19 + -12a + a2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -12a + a2 = 0 + -19
-12a + a2 = 0 + -19

Combine like terms: 0 + -19 = -19
-12a + a2 = -19

The a term is -12a.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12a + 36 + a2 = -19 + 36

Reorder the terms:
36 + -12a + a2 = -19 + 36

Combine like terms: -19 + 36 = 17
36 + -12a + a2 = 17

Factor a perfect square on the left side:
(a + -6)(a + -6) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(a + -6) equal to 4.123105626 and -4.123105626.

Subproblem 1
a + -6 = 4.123105626

Simplifying
a + -6 = 4.123105626

Reorder the terms:
-6 + a = 4.123105626

Solving
-6 + a = 4.123105626

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a = 4.123105626 + 6

Combine like terms: -6 + 6 = 0
0 + a = 4.123105626 + 6
a = 4.123105626 + 6

Combine like terms: 4.123105626 + 6 = 10.123105626
a = 10.123105626

Simplifying
a = 10.123105626

Subproblem 2
a + -6 = -4.123105626

Simplifying
a + -6 = -4.123105626

Reorder the terms:
-6 + a = -4.123105626

Solving
-6 + a = -4.123105626

Solving for variable 'a'.

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

Add '6' to each side of the equation.
-6 + 6 + a = -4.123105626 + 6

Combine like terms: -6 + 6 = 0
0 + a = -4.123105626 + 6
a = -4.123105626 + 6

Combine like terms: -4.123105626 + 6 = 1.876894374
a = 1.876894374

Simplifying
a = 1.876894374

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {10.123105626, 1.876894374}