-7a(a-1)-6(7a-6)=

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Solution for -7a(a-1)-6(7a-6)= equation: 


Simplifying
-7a(a + -1) + -6(7a + -6) = 0

Reorder the terms:
-7a(-1 + a) + -6(7a + -6) = 0
(-1 * -7a + a * -7a) + -6(7a + -6) = 0
(7a + -7a2) + -6(7a + -6) = 0

Reorder the terms:
7a + -7a2 + -6(-6 + 7a) = 0
7a + -7a2 + (-6 * -6 + 7a * -6) = 0
7a + -7a2 + (36 + -42a) = 0

Reorder the terms:
36 + 7a + -42a + -7a2 = 0

Combine like terms: 7a + -42a = -35a
36 + -35a + -7a2 = 0

Solving
36 + -35a + -7a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-5.142857143 + 5a + a2 = 0

Move the constant term to the right:

Add '5.142857143' to each side of the equation.
-5.142857143 + 5a + 5.142857143 + a2 = 0 + 5.142857143

Reorder the terms:
-5.142857143 + 5.142857143 + 5a + a2 = 0 + 5.142857143

Combine like terms: -5.142857143 + 5.142857143 = 0.000000000
0.000000000 + 5a + a2 = 0 + 5.142857143
5a + a2 = 0 + 5.142857143

Combine like terms: 0 + 5.142857143 = 5.142857143
5a + a2 = 5.142857143

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 5.142857143 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 5.142857143 + 6.25

Combine like terms: 5.142857143 + 6.25 = 11.392857143
6.25 + 5a + a2 = 11.392857143

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 11.392857143

Calculate the square root of the right side: 3.375330672

Break this problem into two subproblems by setting 
(a + 2.5) equal to 3.375330672 and -3.375330672.


Subproblem 1
a + 2.5 = 3.375330672

Simplifying
a + 2.5 = 3.375330672

Reorder the terms:
2.5 + a = 3.375330672

Solving
2.5 + a = 3.375330672

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = 3.375330672 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = 3.375330672 + -2.5
a = 3.375330672 + -2.5

Combine like terms: 3.375330672 + -2.5 = 0.875330672
a = 0.875330672

Simplifying
a = 0.875330672


Subproblem 2
a + 2.5 = -3.375330672

Simplifying
a + 2.5 = -3.375330672

Reorder the terms:
2.5 + a = -3.375330672

Solving
2.5 + a = -3.375330672

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = -3.375330672 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = -3.375330672 + -2.5
a = -3.375330672 + -2.5

Combine like terms: -3.375330672 + -2.5 = -5.875330672
a = -5.875330672

Simplifying
a = -5.875330672


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.875330672, -5.875330672}

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