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

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


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

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

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

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

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

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

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

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

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

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

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

Add '-2a2' to each side of the equation.
35 + -3a + 2a2 + -2a2 = 2a + 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
35 + -3a + 0 = 2a + 2a2 + -2a2
35 + -3a = 2a + 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
35 + -3a = 2a + 0
35 + -3a = 2a

Solving
35 + -3a = 2a

Solving for variable 'a'.

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

Add '-2a' to each side of the equation.
35 + -3a + -2a = 2a + -2a

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

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

Add '-35' to each side of the equation.
35 + -35 + -5a = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -5a = 0 + -35
-5a = 0 + -35

Combine like terms: 0 + -35 = -35
-5a = -35

Divide each side by '-5'.
a = 7

Simplifying
a = 7

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