17-2f(5f-62f)=7(2f+3)

Solution for 17-2f(5f-62f)=7(2f+3) equation:

Simplifying
17 + -2f(5f + -62f) = 7(2f + 3)

Combine like terms: 5f + -62f = -57f
17 + -2f(-57f) = 7(2f + 3)

Remove parenthesis around (-57f)
17 + -2f * -57f = 7(2f + 3)

Reorder the terms for easier multiplication:
17 + -2 * -57f * f = 7(2f + 3)

Multiply -2 * -57
17 + 114f * f = 7(2f + 3)

Multiply f * f
17 + 114f2 = 7(2f + 3)

Reorder the terms:
17 + 114f2 = 7(3 + 2f)
17 + 114f2 = (3 * 7 + 2f * 7)
17 + 114f2 = (21 + 14f)

Solving
17 + 114f2 = 21 + 14f

Solving for variable 'f'.

Reorder the terms:
17 + -21 + -14f + 114f2 = 21 + 14f + -21 + -14f

Combine like terms: 17 + -21 = -4
-4 + -14f + 114f2 = 21 + 14f + -21 + -14f

Reorder the terms:
-4 + -14f + 114f2 = 21 + -21 + 14f + -14f

Combine like terms: 21 + -21 = 0
-4 + -14f + 114f2 = 0 + 14f + -14f
-4 + -14f + 114f2 = 14f + -14f

Combine like terms: 14f + -14f = 0
-4 + -14f + 114f2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -7f + 57f2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -7f + 57f2)' equal to zero and attempt to solve:

Simplifying
-2 + -7f + 57f2 = 0

Solving
-2 + -7f + 57f2 = 0

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

Divide each side by '57'.
-0.0350877193 + -0.1228070175f + f2 = 0

Move the constant term to the right:

Add '0.0350877193' to each side of the equation.
-0.0350877193 + -0.1228070175f + 0.0350877193 + f2 = 0 + 0.0350877193

Reorder the terms:
-0.0350877193 + 0.0350877193 + -0.1228070175f + f2 = 0 + 0.0350877193

Combine like terms: -0.0350877193 + 0.0350877193 = 0.0000000000
0.0000000000 + -0.1228070175f + f2 = 0 + 0.0350877193
-0.1228070175f + f2 = 0 + 0.0350877193

Combine like terms: 0 + 0.0350877193 = 0.0350877193
-0.1228070175f + f2 = 0.0350877193

The f term is -0.1228070175f.  Take half its coefficient (-0.06140350875).
Square it (0.003770390887) and add it to both sides.

Add '0.003770390887' to each side of the equation.
-0.1228070175f + 0.003770390887 + f2 = 0.0350877193 + 0.003770390887

Reorder the terms:
0.003770390887 + -0.1228070175f + f2 = 0.0350877193 + 0.003770390887

Combine like terms: 0.0350877193 + 0.003770390887 = 0.038858110187
0.003770390887 + -0.1228070175f + f2 = 0.038858110187

Factor a perfect square on the left side:
(f + -0.06140350875)(f + -0.06140350875) = 0.038858110187

Calculate the square root of the right side: 0.197124606

Break this problem into two subproblems by setting 
(f + -0.06140350875) equal to 0.197124606 and -0.197124606.

Subproblem 1
f + -0.06140350875 = 0.197124606

Simplifying
f + -0.06140350875 = 0.197124606

Reorder the terms:
-0.06140350875 + f = 0.197124606

Solving
-0.06140350875 + f = 0.197124606

Solving for variable 'f'.

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

Add '0.06140350875' to each side of the equation.
-0.06140350875 + 0.06140350875 + f = 0.197124606 + 0.06140350875

Combine like terms: -0.06140350875 + 0.06140350875 = 0.00000000000
0.00000000000 + f = 0.197124606 + 0.06140350875
f = 0.197124606 + 0.06140350875

Combine like terms: 0.197124606 + 0.06140350875 = 0.25852811475
f = 0.25852811475

Simplifying
f = 0.25852811475

Subproblem 2
f + -0.06140350875 = -0.197124606

Simplifying
f + -0.06140350875 = -0.197124606

Reorder the terms:
-0.06140350875 + f = -0.197124606

Solving
-0.06140350875 + f = -0.197124606

Solving for variable 'f'.

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

Add '0.06140350875' to each side of the equation.
-0.06140350875 + 0.06140350875 + f = -0.197124606 + 0.06140350875

Combine like terms: -0.06140350875 + 0.06140350875 = 0.00000000000
0.00000000000 + f = -0.197124606 + 0.06140350875
f = -0.197124606 + 0.06140350875

Combine like terms: -0.197124606 + 0.06140350875 = -0.13572109725
f = -0.13572109725

Simplifying
f = -0.13572109725

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.25852811475, -0.13572109725}
Solution
f = {0.25852811475, -0.13572109725}