f(2c)=5(4c^2)+6(2c)

Solution for f(2c)=5(4c^2)+6(2c) equation:

Simplifying
f(2c) = 5(4c2) + 6(2c)

Remove parenthesis around (2c)
f * 2c = 5(4c2) + 6(2c)

Reorder the terms for easier multiplication:
2f * c = 5(4c2) + 6(2c)

Multiply f * c
2cf = 5(4c2) + 6(2c)

Remove parenthesis around (4c2)
2cf = 5 * 4c2 + 6(2c)

Multiply 5 * 4
2cf = 20c2 + 6(2c)

Remove parenthesis around (2c)
2cf = 20c2 + 6 * 2c

Multiply 6 * 2
2cf = 20c2 + 12c

Reorder the terms:
2cf = 12c + 20c2

Solving
2cf = 12c + 20c2

Solving for variable 'c'.

Reorder the terms:
-12c + 2cf + -20c2 = 12c + 20c2 + -12c + -20c2

Reorder the terms:
-12c + 2cf + -20c2 = 12c + -12c + 20c2 + -20c2

Combine like terms: 12c + -12c = 0
-12c + 2cf + -20c2 = 0 + 20c2 + -20c2
-12c + 2cf + -20c2 = 20c2 + -20c2

Combine like terms: 20c2 + -20c2 = 0
-12c + 2cf + -20c2 = 0

Factor out the Greatest Common Factor (GCF), '2c'.
2c(-6 + f + -10c) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'c' equal to zero and attempt to solve:

Simplifying
c = 0

Solving
c = 0

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

Simplifying
c = 0
Subproblem 2
Set the factor '(-6 + f + -10c)' equal to zero and attempt to solve:

Simplifying
-6 + f + -10c = 0

Reorder the terms:
-6 + -10c + f = 0

Solving
-6 + -10c + f = 0

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

Add '6' to each side of the equation.
-6 + -10c + 6 + f = 0 + 6

Reorder the terms:
-6 + 6 + -10c + f = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -10c + f = 0 + 6
-10c + f = 0 + 6

Combine like terms: 0 + 6 = 6
-10c + f = 6

Add '-1f' to each side of the equation.
-10c + f + -1f = 6 + -1f

Combine like terms: f + -1f = 0
-10c + 0 = 6 + -1f
-10c = 6 + -1f

Divide each side by '-10'.
c = -0.6 + 0.1f

Simplifying
c = -0.6 + 0.1f
Solution
c = {0, -0.6 + 0.1f}