-2a(3a+1)=8

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Solution for -2a(3a+1)=8 equation: 


Simplifying
-2a(3a + 1) = 8

Reorder the terms:
-2a(1 + 3a) = 8
(1 * -2a + 3a * -2a) = 8
(-2a + -6a2) = 8

Solving
-2a + -6a2 = 8

Solving for variable 'a'.

Reorder the terms:
-8 + -2a + -6a2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -2a + -6a2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(4 + a + 3a2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(4 + a + 3a2)' equal to zero and attempt to solve:

Simplifying
4 + a + 3a2 = 0

Solving
4 + a + 3a2 = 0

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

Divide each side by '3'.
1.333333333 + 0.3333333333a + a2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 0.3333333333a + -1.333333333 + a2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 0.3333333333a + a2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 0.3333333333a + a2 = 0 + -1.333333333
0.3333333333a + a2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
0.3333333333a + a2 = -1.333333333

The a term is a.  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.
0.3333333333a + 0.25 + a2 = -1.333333333 + 0.25

Reorder the terms:
0.25 + 0.3333333333a + a2 = -1.333333333 + 0.25

Combine like terms: -1.333333333 + 0.25 = -1.083333333
0.25 + 0.3333333333a + a2 = -1.083333333

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -1.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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