10(a+6)a=-(4-a)

Solution for 10(a+6)a=-(4-a) equation:

Simplifying
10(a + 6) * a = -1(4 + -1a)

Reorder the terms:
10(6 + a) * a = -1(4 + -1a)

Reorder the terms for easier multiplication:
10a(6 + a) = -1(4 + -1a)
(6 * 10a + a * 10a) = -1(4 + -1a)
(60a + 10a2) = -1(4 + -1a)
60a + 10a2 = (4 * -1 + -1a * -1)
60a + 10a2 = (-4 + 1a)

Solving
60a + 10a2 = -4 + 1a

Solving for variable 'a'.

Reorder the terms:
4 + 60a + -1a + 10a2 = -4 + 1a + 4 + -1a

Combine like terms: 60a + -1a = 59a
4 + 59a + 10a2 = -4 + 1a + 4 + -1a

Reorder the terms:
4 + 59a + 10a2 = -4 + 4 + 1a + -1a

Combine like terms: -4 + 4 = 0
4 + 59a + 10a2 = 0 + 1a + -1a
4 + 59a + 10a2 = 1a + -1a

Combine like terms: 1a + -1a = 0
4 + 59a + 10a2 = 0

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

Divide each side by '10'.
0.4 + 5.9a + a2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 5.9a + -0.4 + a2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 5.9a + a2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 5.9a + a2 = 0 + -0.4
5.9a + a2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
5.9a + a2 = -0.4

The a term is 5.9a.  Take half its coefficient (2.95).
Square it (8.7025) and add it to both sides.

Add '8.7025' to each side of the equation.
5.9a + 8.7025 + a2 = -0.4 + 8.7025

Reorder the terms:
8.7025 + 5.9a + a2 = -0.4 + 8.7025

Combine like terms: -0.4 + 8.7025 = 8.3025
8.7025 + 5.9a + a2 = 8.3025

Factor a perfect square on the left side:
(a + 2.95)(a + 2.95) = 8.3025

Calculate the square root of the right side: 2.881405907

Break this problem into two subproblems by setting 
(a + 2.95) equal to 2.881405907 and -2.881405907.

Subproblem 1
a + 2.95 = 2.881405907

Simplifying
a + 2.95 = 2.881405907

Reorder the terms:
2.95 + a = 2.881405907

Solving
2.95 + a = 2.881405907

Solving for variable 'a'.

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

Add '-2.95' to each side of the equation.
2.95 + -2.95 + a = 2.881405907 + -2.95

Combine like terms: 2.95 + -2.95 = 0.00
0.00 + a = 2.881405907 + -2.95
a = 2.881405907 + -2.95

Combine like terms: 2.881405907 + -2.95 = -0.068594093
a = -0.068594093

Simplifying
a = -0.068594093

Subproblem 2
a + 2.95 = -2.881405907

Simplifying
a + 2.95 = -2.881405907

Reorder the terms:
2.95 + a = -2.881405907

Solving
2.95 + a = -2.881405907

Solving for variable 'a'.

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

Add '-2.95' to each side of the equation.
2.95 + -2.95 + a = -2.881405907 + -2.95

Combine like terms: 2.95 + -2.95 = 0.00
0.00 + a = -2.881405907 + -2.95
a = -2.881405907 + -2.95

Combine like terms: -2.881405907 + -2.95 = -5.831405907
a = -5.831405907

Simplifying
a = -5.831405907

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.068594093, -5.831405907}