a+(a-3)=(a+4)-(a-1)(a+2)

Solution for a+(a-3)=(a+4)-(a-1)(a+2) equation:

Simplifying
a + (a + -3) = (a + 4) + -1(a + -1)(a + 2)

Reorder the terms:
a + (-3 + a) = (a + 4) + -1(a + -1)(a + 2)

Remove parenthesis around (-3 + a)
a + -3 + a = (a + 4) + -1(a + -1)(a + 2)

Reorder the terms:
-3 + a + a = (a + 4) + -1(a + -1)(a + 2)

Combine like terms: a + a = 2a
-3 + 2a = (a + 4) + -1(a + -1)(a + 2)

Reorder the terms:
-3 + 2a = (4 + a) + -1(a + -1)(a + 2)

Remove parenthesis around (4 + a)
-3 + 2a = 4 + a + -1(a + -1)(a + 2)

Reorder the terms:
-3 + 2a = 4 + a + -1(-1 + a)(a + 2)

Reorder the terms:
-3 + 2a = 4 + a + -1(-1 + a)(2 + a)

Multiply (-1 + a) * (2 + a)
-3 + 2a = 4 + a + -1(-1(2 + a) + a(2 + a))
-3 + 2a = 4 + a + -1((2 * -1 + a * -1) + a(2 + a))
-3 + 2a = 4 + a + -1((-2 + -1a) + a(2 + a))
-3 + 2a = 4 + a + -1(-2 + -1a + (2 * a + a * a))
-3 + 2a = 4 + a + -1(-2 + -1a + (2a + a2))

Combine like terms: -1a + 2a = 1a
-3 + 2a = 4 + a + -1(-2 + 1a + a2)
-3 + 2a = 4 + a + (-2 * -1 + 1a * -1 + a2 * -1)
-3 + 2a = 4 + a + (2 + -1a + -1a2)

Reorder the terms:
-3 + 2a = 4 + 2 + a + -1a + -1a2

Combine like terms: 4 + 2 = 6
-3 + 2a = 6 + a + -1a + -1a2

Combine like terms: a + -1a = 0
-3 + 2a = 6 + 0 + -1a2
-3 + 2a = 6 + -1a2

Solving
-3 + 2a = 6 + -1a2

Solving for variable 'a'.

Reorder the terms:
-3 + -6 + 2a + a2 = 6 + -1a2 + -6 + a2

Combine like terms: -3 + -6 = -9
-9 + 2a + a2 = 6 + -1a2 + -6 + a2

Reorder the terms:
-9 + 2a + a2 = 6 + -6 + -1a2 + a2

Combine like terms: 6 + -6 = 0
-9 + 2a + a2 = 0 + -1a2 + a2
-9 + 2a + a2 = -1a2 + a2

Combine like terms: -1a2 + a2 = 0
-9 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + 2a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2a + a2 = 0 + 9
2a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
2a + a2 = 9

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 = 9 + 1

Reorder the terms:
1 + 2a + a2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2a + a2 = 10

Factor a perfect square on the left side:
(a + 1)(a + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(a + 1) equal to 3.16227766 and -3.16227766.

Subproblem 1
a + 1 = 3.16227766

Simplifying
a + 1 = 3.16227766

Reorder the terms:
1 + a = 3.16227766

Solving
1 + a = 3.16227766

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 = 3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + a = 3.16227766 + -1
a = 3.16227766 + -1

Combine like terms: 3.16227766 + -1 = 2.16227766
a = 2.16227766

Simplifying
a = 2.16227766

Subproblem 2
a + 1 = -3.16227766

Simplifying
a + 1 = -3.16227766

Reorder the terms:
1 + a = -3.16227766

Solving
1 + a = -3.16227766

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 = -3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + a = -3.16227766 + -1
a = -3.16227766 + -1

Combine like terms: -3.16227766 + -1 = -4.16227766
a = -4.16227766

Simplifying
a = -4.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.16227766, -4.16227766}