8-2(a-6)=-4-3a(a+5)

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Solution for 8-2(a-6)=-4-3a(a+5) equation: 


Simplifying
8 + -2(a + -6) = -4 + -3a(a + 5)

Reorder the terms:
8 + -2(-6 + a) = -4 + -3a(a + 5)
8 + (-6 * -2 + a * -2) = -4 + -3a(a + 5)
8 + (12 + -2a) = -4 + -3a(a + 5)

Combine like terms: 8 + 12 = 20
20 + -2a = -4 + -3a(a + 5)

Reorder the terms:
20 + -2a = -4 + -3a(5 + a)
20 + -2a = -4 + (5 * -3a + a * -3a)
20 + -2a = -4 + (-15a + -3a2)

Solving
20 + -2a = -4 + -15a + -3a2

Solving for variable 'a'.

Reorder the terms:
20 + 4 + -2a + 15a + 3a2 = -4 + -15a + -3a2 + 4 + 15a + 3a2

Combine like terms: 20 + 4 = 24
24 + -2a + 15a + 3a2 = -4 + -15a + -3a2 + 4 + 15a + 3a2

Combine like terms: -2a + 15a = 13a
24 + 13a + 3a2 = -4 + -15a + -3a2 + 4 + 15a + 3a2

Reorder the terms:
24 + 13a + 3a2 = -4 + 4 + -15a + 15a + -3a2 + 3a2

Combine like terms: -4 + 4 = 0
24 + 13a + 3a2 = 0 + -15a + 15a + -3a2 + 3a2
24 + 13a + 3a2 = -15a + 15a + -3a2 + 3a2

Combine like terms: -15a + 15a = 0
24 + 13a + 3a2 = 0 + -3a2 + 3a2
24 + 13a + 3a2 = -3a2 + 3a2

Combine like terms: -3a2 + 3a2 = 0
24 + 13a + 3a2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
8 + 4.333333333a + a2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 4.333333333a + -8 + a2 = 0 + -8

Reorder the terms:
8 + -8 + 4.333333333a + a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 4.333333333a + a2 = 0 + -8
4.333333333a + a2 = 0 + -8

Combine like terms: 0 + -8 = -8
4.333333333a + a2 = -8

The a term is 4.333333333a.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333a + 4.694444446 + a2 = -8 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333a + a2 = -8 + 4.694444446

Combine like terms: -8 + 4.694444446 = -3.305555554
4.694444446 + 4.333333333a + a2 = -3.305555554

Factor a perfect square on the left side:
(a + 2.166666667)(a + 2.166666667) = -3.305555554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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