-2(a^2+3a-84)=0

Solution for -2(a^2+3a-84)=0 equation:

Simplifying
-2(a2 + 3a + -84) = 0

Reorder the terms:
-2(-84 + 3a + a2) = 0
(-84 * -2 + 3a * -2 + a2 * -2) = 0
(168 + -6a + -2a2) = 0

Solving
168 + -6a + -2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(84 + -3a + -1a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(84 + -3a + -1a2)' equal to zero and attempt to solve:

Simplifying
84 + -3a + -1a2 = 0

Solving
84 + -3a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-84 + 3a + a2 = 0

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 3a + 84 + a2 = 0 + 84

Reorder the terms:
-84 + 84 + 3a + a2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 3a + a2 = 0 + 84
3a + a2 = 0 + 84

Combine like terms: 0 + 84 = 84
3a + a2 = 84

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 84 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 84 + 2.25

Combine like terms: 84 + 2.25 = 86.25
2.25 + 3a + a2 = 86.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 86.25

Calculate the square root of the right side: 9.287087811

Break this problem into two subproblems by setting 
(a + 1.5) equal to 9.287087811 and -9.287087811.

Subproblem 1
a + 1.5 = 9.287087811

Simplifying
a + 1.5 = 9.287087811

Reorder the terms:
1.5 + a = 9.287087811

Solving
1.5 + a = 9.287087811

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 9.287087811 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 9.287087811 + -1.5
a = 9.287087811 + -1.5

Combine like terms: 9.287087811 + -1.5 = 7.787087811
a = 7.787087811

Simplifying
a = 7.787087811

Subproblem 2
a + 1.5 = -9.287087811

Simplifying
a + 1.5 = -9.287087811

Reorder the terms:
1.5 + a = -9.287087811

Solving
1.5 + a = -9.287087811

Solving for variable 'a'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -9.287087811 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -9.287087811 + -1.5
a = -9.287087811 + -1.5

Combine like terms: -9.287087811 + -1.5 = -10.787087811
a = -10.787087811

Simplifying
a = -10.787087811

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.787087811, -10.787087811}
Solution
a = {7.787087811, -10.787087811}