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

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

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

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

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

Multiply (3 + 2a) * (-1 + a)
(3(-1 + a) + 2a * (-1 + a)) = 2
((-1 * 3 + a * 3) + 2a * (-1 + a)) = 2
((-3 + 3a) + 2a * (-1 + a)) = 2
(-3 + 3a + (-1 * 2a + a * 2a)) = 2
(-3 + 3a + (-2a + 2a2)) = 2

Combine like terms: 3a + -2a = 1a
(-3 + 1a + 2a2) = 2

Solving
-3 + 1a + 2a2 = 2

Solving for variable 'a'.

Reorder the terms:
-3 + -2 + 1a + 2a2 = 2 + -2

Combine like terms: -3 + -2 = -5
-5 + 1a + 2a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-5 + 1a + 2a2 = 0

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

Divide each side by '2'.
-2.5 + 0.5a + a2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.5a + 2.5 + a2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.5a + a2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.5a + a2 = 0 + 2.5
0.5a + a2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.5a + a2 = 2.5

The a term is 0.5a.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5a + 0.0625 + a2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + 0.5a + a2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + 0.5a + a2 = 2.5625

Factor a perfect square on the left side:
(a + 0.25)(a + 0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(a + 0.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
a + 0.25 = 1.600781059

Simplifying
a + 0.25 = 1.600781059

Reorder the terms:
0.25 + a = 1.600781059

Solving
0.25 + a = 1.600781059

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = 1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = 1.600781059 + -0.25
a = 1.600781059 + -0.25

Combine like terms: 1.600781059 + -0.25 = 1.350781059
a = 1.350781059

Simplifying
a = 1.350781059

Subproblem 2
a + 0.25 = -1.600781059

Simplifying
a + 0.25 = -1.600781059

Reorder the terms:
0.25 + a = -1.600781059

Solving
0.25 + a = -1.600781059

Solving for variable 'a'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + a = -1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + a = -1.600781059 + -0.25
a = -1.600781059 + -0.25

Combine like terms: -1.600781059 + -0.25 = -1.850781059
a = -1.850781059

Simplifying
a = -1.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.350781059, -1.850781059}