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

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

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

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

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

Multiply (5 + a) * (-2 + a)
(5(-2 + a) + a(-2 + a)) = (a + 1)
((-2 * 5 + a * 5) + a(-2 + a)) = (a + 1)
((-10 + 5a) + a(-2 + a)) = (a + 1)
(-10 + 5a + (-2 * a + a * a)) = (a + 1)
(-10 + 5a + (-2a + a2)) = (a + 1)

Combine like terms: 5a + -2a = 3a
(-10 + 3a + a2) = (a + 1)

Reorder the terms:
-10 + 3a + a2 = (1 + a)

Remove parenthesis around (1 + a)
-10 + 3a + a2 = 1 + a

Solving
-10 + 3a + a2 = 1 + a

Solving for variable 'a'.

Reorder the terms:
-10 + -1 + 3a + -1a + a2 = 1 + a + -1 + -1a

Combine like terms: -10 + -1 = -11
-11 + 3a + -1a + a2 = 1 + a + -1 + -1a

Combine like terms: 3a + -1a = 2a
-11 + 2a + a2 = 1 + a + -1 + -1a

Reorder the terms:
-11 + 2a + a2 = 1 + -1 + a + -1a

Combine like terms: 1 + -1 = 0
-11 + 2a + a2 = 0 + a + -1a
-11 + 2a + a2 = a + -1a

Combine like terms: a + -1a = 0
-11 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 2a + 11 + a2 = 0 + 11

Reorder the terms:
-11 + 11 + 2a + a2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2a + a2 = 0 + 11
2a + a2 = 0 + 11

Combine like terms: 0 + 11 = 11
2a + a2 = 11

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 11 + 1

Reorder the terms:
1 + 2a + a2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + 2a + a2 = 12

Factor a perfect square on the left side:
(a + 1)(a + 1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(a + 1) equal to 3.464101615 and -3.464101615.

Subproblem 1
a + 1 = 3.464101615

Simplifying
a + 1 = 3.464101615

Reorder the terms:
1 + a = 3.464101615

Solving
1 + a = 3.464101615

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + a = 3.464101615 + -1
a = 3.464101615 + -1

Combine like terms: 3.464101615 + -1 = 2.464101615
a = 2.464101615

Simplifying
a = 2.464101615

Subproblem 2
a + 1 = -3.464101615

Simplifying
a + 1 = -3.464101615

Reorder the terms:
1 + a = -3.464101615

Solving
1 + a = -3.464101615

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + a = -3.464101615 + -1
a = -3.464101615 + -1

Combine like terms: -3.464101615 + -1 = -4.464101615
a = -4.464101615

Simplifying
a = -4.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.464101615, -4.464101615}