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

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

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

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

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

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

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

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

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

Multiply 5 * 2
2cf = 4c2 + 10c

Reorder the terms:
2cf = 10c + 4c2

Solving
2cf = 10c + 4c2

Solving for variable 'c'.

Reorder the terms:
-10c + 2cf + -4c2 = 10c + 4c2 + -10c + -4c2

Reorder the terms:
-10c + 2cf + -4c2 = 10c + -10c + 4c2 + -4c2

Combine like terms: 10c + -10c = 0
-10c + 2cf + -4c2 = 0 + 4c2 + -4c2
-10c + 2cf + -4c2 = 4c2 + -4c2

Combine like terms: 4c2 + -4c2 = 0
-10c + 2cf + -4c2 = 0

Factor out the Greatest Common Factor (GCF), '2c'.
2c(-5 + f + -2c) = 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 '(-5 + f + -2c)' equal to zero and attempt to solve:

Simplifying
-5 + f + -2c = 0

Reorder the terms:
-5 + -2c + f = 0

Solving
-5 + -2c + f = 0

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

Add '5' to each side of the equation.
-5 + -2c + 5 + f = 0 + 5

Reorder the terms:
-5 + 5 + -2c + f = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2c + f = 0 + 5
-2c + f = 0 + 5

Combine like terms: 0 + 5 = 5
-2c + f = 5

Add '-1f' to each side of the equation.
-2c + f + -1f = 5 + -1f

Combine like terms: f + -1f = 0
-2c + 0 = 5 + -1f
-2c = 5 + -1f

Divide each side by '-2'.
c = -2.5 + 0.5f

Simplifying
c = -2.5 + 0.5f
Solution
c = {0, -2.5 + 0.5f}