2f(5f-2)-10(f^2-3f+6)=-8f(f+4)+(2f^2-7f)

Solution for 2f(5f-2)-10(f^2-3f+6)=-8f(f+4)+(2f^2-7f) equation:

Simplifying
2f(5f + -2) + -10(f2 + -3f + 6) = -8f(f + 4) + (2f2 + -7f)

Reorder the terms:
2f(-2 + 5f) + -10(f2 + -3f + 6) = -8f(f + 4) + (2f2 + -7f)
(-2 * 2f + 5f * 2f) + -10(f2 + -3f + 6) = -8f(f + 4) + (2f2 + -7f)
(-4f + 10f2) + -10(f2 + -3f + 6) = -8f(f + 4) + (2f2 + -7f)

Reorder the terms:
-4f + 10f2 + -10(6 + -3f + f2) = -8f(f + 4) + (2f2 + -7f)
-4f + 10f2 + (6 * -10 + -3f * -10 + f2 * -10) = -8f(f + 4) + (2f2 + -7f)
-4f + 10f2 + (-60 + 30f + -10f2) = -8f(f + 4) + (2f2 + -7f)

Reorder the terms:
-60 + -4f + 30f + 10f2 + -10f2 = -8f(f + 4) + (2f2 + -7f)

Combine like terms: -4f + 30f = 26f
-60 + 26f + 10f2 + -10f2 = -8f(f + 4) + (2f2 + -7f)

Combine like terms: 10f2 + -10f2 = 0
-60 + 26f + 0 = -8f(f + 4) + (2f2 + -7f)
-60 + 26f = -8f(f + 4) + (2f2 + -7f)

Reorder the terms:
-60 + 26f = -8f(4 + f) + (2f2 + -7f)
-60 + 26f = (4 * -8f + f * -8f) + (2f2 + -7f)
-60 + 26f = (-32f + -8f2) + (2f2 + -7f)

Reorder the terms:
-60 + 26f = -32f + -8f2 + (-7f + 2f2)

Remove parenthesis around (-7f + 2f2)
-60 + 26f = -32f + -8f2 + -7f + 2f2

Reorder the terms:
-60 + 26f = -32f + -7f + -8f2 + 2f2

Combine like terms: -32f + -7f = -39f
-60 + 26f = -39f + -8f2 + 2f2

Combine like terms: -8f2 + 2f2 = -6f2
-60 + 26f = -39f + -6f2

Solving
-60 + 26f = -39f + -6f2

Solving for variable 'f'.

Combine like terms: 26f + 39f = 65f
-60 + 65f + 6f2 = -39f + -6f2 + 39f + 6f2

Reorder the terms:
-60 + 65f + 6f2 = -39f + 39f + -6f2 + 6f2

Combine like terms: -39f + 39f = 0
-60 + 65f + 6f2 = 0 + -6f2 + 6f2
-60 + 65f + 6f2 = -6f2 + 6f2

Combine like terms: -6f2 + 6f2 = 0
-60 + 65f + 6f2 = 0

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

Divide each side by '6'.
-10 + 10.83333333f + f2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 10.83333333f + 10 + f2 = 0 + 10

Reorder the terms:
-10 + 10 + 10.83333333f + f2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 10.83333333f + f2 = 0 + 10
10.83333333f + f2 = 0 + 10

Combine like terms: 0 + 10 = 10
10.83333333f + f2 = 10

The f term is 10.83333333f.  Take half its coefficient (5.416666665).
Square it (29.34027776) and add it to both sides.

Add '29.34027776' to each side of the equation.
10.83333333f + 29.34027776 + f2 = 10 + 29.34027776

Reorder the terms:
29.34027776 + 10.83333333f + f2 = 10 + 29.34027776

Combine like terms: 10 + 29.34027776 = 39.34027776
29.34027776 + 10.83333333f + f2 = 39.34027776

Factor a perfect square on the left side:
(f + 5.416666665)(f + 5.416666665) = 39.34027776

Calculate the square root of the right side: 6.272182854

Break this problem into two subproblems by setting 
(f + 5.416666665) equal to 6.272182854 and -6.272182854.

Subproblem 1
f + 5.416666665 = 6.272182854

Simplifying
f + 5.416666665 = 6.272182854

Reorder the terms:
5.416666665 + f = 6.272182854

Solving
5.416666665 + f = 6.272182854

Solving for variable 'f'.

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

Add '-5.416666665' to each side of the equation.
5.416666665 + -5.416666665 + f = 6.272182854 + -5.416666665

Combine like terms: 5.416666665 + -5.416666665 = 0.000000000
0.000000000 + f = 6.272182854 + -5.416666665
f = 6.272182854 + -5.416666665

Combine like terms: 6.272182854 + -5.416666665 = 0.855516189
f = 0.855516189

Simplifying
f = 0.855516189

Subproblem 2
f + 5.416666665 = -6.272182854

Simplifying
f + 5.416666665 = -6.272182854

Reorder the terms:
5.416666665 + f = -6.272182854

Solving
5.416666665 + f = -6.272182854

Solving for variable 'f'.

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

Add '-5.416666665' to each side of the equation.
5.416666665 + -5.416666665 + f = -6.272182854 + -5.416666665

Combine like terms: 5.416666665 + -5.416666665 = 0.000000000
0.000000000 + f = -6.272182854 + -5.416666665
f = -6.272182854 + -5.416666665

Combine like terms: -6.272182854 + -5.416666665 = -11.688849519
f = -11.688849519

Simplifying
f = -11.688849519

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.855516189, -11.688849519}