a(a+3)+a(a-6)+35=a(a-5)+(a+7)

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Solution for a(a+3)+a(a-6)+35=a(a-5)+(a+7) equation: 


Simplifying
a(a + 3) + a(a + -6) + 35 = a(a + -5) + (a + 7)

Reorder the terms:
a(3 + a) + a(a + -6) + 35 = a(a + -5) + (a + 7)
(3 * a + a * a) + a(a + -6) + 35 = a(a + -5) + (a + 7)
(3a + a2) + a(a + -6) + 35 = a(a + -5) + (a + 7)

Reorder the terms:
3a + a2 + a(-6 + a) + 35 = a(a + -5) + (a + 7)
3a + a2 + (-6 * a + a * a) + 35 = a(a + -5) + (a + 7)
3a + a2 + (-6a + a2) + 35 = a(a + -5) + (a + 7)

Reorder the terms:
35 + 3a + -6a + a2 + a2 = a(a + -5) + (a + 7)

Combine like terms: 3a + -6a = -3a
35 + -3a + a2 + a2 = a(a + -5) + (a + 7)

Combine like terms: a2 + a2 = 2a2
35 + -3a + 2a2 = a(a + -5) + (a + 7)

Reorder the terms:
35 + -3a + 2a2 = a(-5 + a) + (a + 7)
35 + -3a + 2a2 = (-5 * a + a * a) + (a + 7)
35 + -3a + 2a2 = (-5a + a2) + (a + 7)

Reorder the terms:
35 + -3a + 2a2 = -5a + a2 + (7 + a)

Remove parenthesis around (7 + a)
35 + -3a + 2a2 = -5a + a2 + 7 + a

Reorder the terms:
35 + -3a + 2a2 = 7 + -5a + a + a2

Combine like terms: -5a + a = -4a
35 + -3a + 2a2 = 7 + -4a + a2

Solving
35 + -3a + 2a2 = 7 + -4a + a2

Solving for variable 'a'.

Reorder the terms:
35 + -7 + -3a + 4a + 2a2 + -1a2 = 7 + -4a + a2 + -7 + 4a + -1a2

Combine like terms: 35 + -7 = 28
28 + -3a + 4a + 2a2 + -1a2 = 7 + -4a + a2 + -7 + 4a + -1a2

Combine like terms: -3a + 4a = 1a
28 + 1a + 2a2 + -1a2 = 7 + -4a + a2 + -7 + 4a + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
28 + 1a + 1a2 = 7 + -4a + a2 + -7 + 4a + -1a2

Reorder the terms:
28 + 1a + 1a2 = 7 + -7 + -4a + 4a + a2 + -1a2

Combine like terms: 7 + -7 = 0
28 + 1a + 1a2 = 0 + -4a + 4a + a2 + -1a2
28 + 1a + 1a2 = -4a + 4a + a2 + -1a2

Combine like terms: -4a + 4a = 0
28 + 1a + 1a2 = 0 + a2 + -1a2
28 + 1a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
28 + 1a + 1a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 1a + -28 + a2 = 0 + -28

Reorder the terms:
28 + -28 + 1a + a2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 1a + a2 = 0 + -28
1a + a2 = 0 + -28

Combine like terms: 0 + -28 = -28
1a + a2 = -28

The a term is 1a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
a + 0.25 + a2 = -28 + 0.25

Reorder the terms:
0.25 + a + a2 = -28 + 0.25

Combine like terms: -28 + 0.25 = -27.75
0.25 + a + a2 = -27.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -27.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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