a(a+3)+a(a-6)+35=a(a-5)

Solution for a(a+3)+a(a-6)+35=a(a-5) equation:

Simplifying
a(a + 3) + a(a + -6) + 35 = a(a + -5)

Reorder the terms:
a(3 + a) + a(a + -6) + 35 = a(a + -5)
(3 * a + a * a) + a(a + -6) + 35 = a(a + -5)
(3a + a2) + a(a + -6) + 35 = a(a + -5)

Reorder the terms:
3a + a2 + a(-6 + a) + 35 = a(a + -5)
3a + a2 + (-6 * a + a * a) + 35 = a(a + -5)
3a + a2 + (-6a + a2) + 35 = a(a + -5)

Reorder the terms:
35 + 3a + -6a + a2 + a2 = a(a + -5)

Combine like terms: 3a + -6a = -3a
35 + -3a + a2 + a2 = a(a + -5)

Combine like terms: a2 + a2 = 2a2
35 + -3a + 2a2 = a(a + -5)

Reorder the terms:
35 + -3a + 2a2 = a(-5 + a)
35 + -3a + 2a2 = (-5 * a + a * a)
35 + -3a + 2a2 = (-5a + a2)

Solving
35 + -3a + 2a2 = -5a + a2

Solving for variable 'a'.

Reorder the terms:
35 + -3a + 5a + 2a2 + -1a2 = -5a + a2 + 5a + -1a2

Combine like terms: -3a + 5a = 2a
35 + 2a + 2a2 + -1a2 = -5a + a2 + 5a + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
35 + 2a + 1a2 = -5a + a2 + 5a + -1a2

Reorder the terms:
35 + 2a + 1a2 = -5a + 5a + a2 + -1a2

Combine like terms: -5a + 5a = 0
35 + 2a + 1a2 = 0 + a2 + -1a2
35 + 2a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
35 + 2a + 1a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 2a + -35 + a2 = 0 + -35

Reorder the terms:
35 + -35 + 2a + a2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 2a + a2 = 0 + -35
2a + a2 = 0 + -35

Combine like terms: 0 + -35 = -35
2a + a2 = -35

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 = -35 + 1

Reorder the terms:
1 + 2a + a2 = -35 + 1

Combine like terms: -35 + 1 = -34
1 + 2a + a2 = -34

Factor a perfect square on the left side:
(a + 1)(a + 1) = -34

Can't calculate square root of the right side.

The solution to this equation could not be determined.