-4[3a(6-a)+2(a^2-4)+1]=

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Solution for -4[3a(6-a)+2(a^2-4)+1]= equation: 


Simplifying
-4[3a(6 + -1a) + 2(a2 + -4) + 1] = 0
-4[(6 * 3a + -1a * 3a) + 2(a2 + -4) + 1] = 0
-4[(18a + -3a2) + 2(a2 + -4) + 1] = 0

Reorder the terms:
-4[18a + -3a2 + 2(-4 + a2) + 1] = 0
-4[18a + -3a2 + (-4 * 2 + a2 * 2) + 1] = 0
-4[18a + -3a2 + (-8 + 2a2) + 1] = 0

Reorder the terms:
-4[-8 + 1 + 18a + -3a2 + 2a2] = 0

Combine like terms: -8 + 1 = -7
-4[-7 + 18a + -3a2 + 2a2] = 0

Combine like terms: -3a2 + 2a2 = -1a2
-4[-7 + 18a + -1a2] = 0
[-7 * -4 + 18a * -4 + -1a2 * -4] = 0
[28 + -72a + 4a2] = 0

Solving
28 + -72a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -18a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + -18a + a2)' equal to zero and attempt to solve:

Simplifying
7 + -18a + a2 = 0

Solving
7 + -18a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -18a + -7 + a2 = 0 + -7

Reorder the terms:
7 + -7 + -18a + a2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -18a + a2 = 0 + -7
-18a + a2 = 0 + -7

Combine like terms: 0 + -7 = -7
-18a + a2 = -7

The a term is -18a.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18a + 81 + a2 = -7 + 81

Reorder the terms:
81 + -18a + a2 = -7 + 81

Combine like terms: -7 + 81 = 74
81 + -18a + a2 = 74

Factor a perfect square on the left side:
(a + -9)(a + -9) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(a + -9) equal to 8.602325267 and -8.602325267.


Subproblem 1
a + -9 = 8.602325267

Simplifying
a + -9 = 8.602325267

Reorder the terms:
-9 + a = 8.602325267

Solving
-9 + a = 8.602325267

Solving for variable 'a'.

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

Add '9' to each side of the equation.
-9 + 9 + a = 8.602325267 + 9

Combine like terms: -9 + 9 = 0
0 + a = 8.602325267 + 9
a = 8.602325267 + 9

Combine like terms: 8.602325267 + 9 = 17.602325267
a = 17.602325267

Simplifying
a = 17.602325267


Subproblem 2
a + -9 = -8.602325267

Simplifying
a + -9 = -8.602325267

Reorder the terms:
-9 + a = -8.602325267

Solving
-9 + a = -8.602325267

Solving for variable 'a'.

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

Add '9' to each side of the equation.
-9 + 9 + a = -8.602325267 + 9

Combine like terms: -9 + 9 = 0
0 + a = -8.602325267 + 9
a = -8.602325267 + 9

Combine like terms: -8.602325267 + 9 = 0.397674733
a = 0.397674733

Simplifying
a = 0.397674733


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {17.602325267, 0.397674733}
Solution
a = {17.602325267, 0.397674733}

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