6a-10a-3a(2a)=[-25-25]-5(8)

Solution for 6a-10a-3a(2a)=[-25-25]-5(8) equation:

Simplifying
6a + -10a + -3a(2a) = [-25 + -25] + -5(8)

Remove parenthesis around (2a)
6a + -10a + -3a * 2a = [-25 + -25] + -5(8)

Reorder the terms for easier multiplication:
6a + -10a + -3 * 2a * a = [-25 + -25] + -5(8)

Multiply -3 * 2
6a + -10a + -6a * a = [-25 + -25] + -5(8)

Multiply a * a
6a + -10a + -6a2 = [-25 + -25] + -5(8)

Combine like terms: 6a + -10a = -4a
-4a + -6a2 = [-25 + -25] + -5(8)

Combine like terms: -25 + -25 = -50
-4a + -6a2 = [-50] + -5(8)
-4a + -6a2 = -50 + -5(8)

Multiply -5 * 8
-4a + -6a2 = -50 + -40

Combine like terms: -50 + -40 = -90
-4a + -6a2 = -90

Solving
-4a + -6a2 = -90

Solving for variable 'a'.

Reorder the terms:
90 + -4a + -6a2 = -90 + 90

Combine like terms: -90 + 90 = 0
90 + -4a + -6a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -2a + -3a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(45 + -2a + -3a2)' equal to zero and attempt to solve:

Simplifying
45 + -2a + -3a2 = 0

Solving
45 + -2a + -3a2 = 0

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

Divide each side by '-3'.
-15 + 0.6666666667a + a2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 0.6666666667a + 15 + a2 = 0 + 15

Reorder the terms:
-15 + 15 + 0.6666666667a + a2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 0.6666666667a + a2 = 0 + 15
0.6666666667a + a2 = 0 + 15

Combine like terms: 0 + 15 = 15
0.6666666667a + a2 = 15

The a term is 0.6666666667a.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667a + 0.1111111112 + a2 = 15 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667a + a2 = 15 + 0.1111111112

Combine like terms: 15 + 0.1111111112 = 15.1111111112
0.1111111112 + 0.6666666667a + a2 = 15.1111111112

Factor a perfect square on the left side:
(a + 0.3333333334)(a + 0.3333333334) = 15.1111111112

Calculate the square root of the right side: 3.887301263

Break this problem into two subproblems by setting 
(a + 0.3333333334) equal to 3.887301263 and -3.887301263.

Subproblem 1
a + 0.3333333334 = 3.887301263

Simplifying
a + 0.3333333334 = 3.887301263

Reorder the terms:
0.3333333334 + a = 3.887301263

Solving
0.3333333334 + a = 3.887301263

Solving for variable 'a'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + a = 3.887301263 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + a = 3.887301263 + -0.3333333334
a = 3.887301263 + -0.3333333334

Combine like terms: 3.887301263 + -0.3333333334 = 3.5539679296
a = 3.5539679296

Simplifying
a = 3.5539679296

Subproblem 2
a + 0.3333333334 = -3.887301263

Simplifying
a + 0.3333333334 = -3.887301263

Reorder the terms:
0.3333333334 + a = -3.887301263

Solving
0.3333333334 + a = -3.887301263

Solving for variable 'a'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + a = -3.887301263 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + a = -3.887301263 + -0.3333333334
a = -3.887301263 + -0.3333333334

Combine like terms: -3.887301263 + -0.3333333334 = -4.2206345964
a = -4.2206345964

Simplifying
a = -4.2206345964

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.5539679296, -4.2206345964}
Solution
a = {3.5539679296, -4.2206345964}