f(2a)=5(2a^2)+4(2a)

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

Simplifying
f(2a) = 5(2a2) + 4(2a)

Remove parenthesis around (2a)
f * 2a = 5(2a2) + 4(2a)

Reorder the terms for easier multiplication:
2f * a = 5(2a2) + 4(2a)

Multiply f * a
2af = 5(2a2) + 4(2a)

Remove parenthesis around (2a2)
2af = 5 * 2a2 + 4(2a)

Multiply 5 * 2
2af = 10a2 + 4(2a)

Remove parenthesis around (2a)
2af = 10a2 + 4 * 2a

Multiply 4 * 2
2af = 10a2 + 8a

Reorder the terms:
2af = 8a + 10a2

Solving
2af = 8a + 10a2

Solving for variable 'a'.

Reorder the terms:
-8a + 2af + -10a2 = 8a + 10a2 + -8a + -10a2

Reorder the terms:
-8a + 2af + -10a2 = 8a + -8a + 10a2 + -10a2

Combine like terms: 8a + -8a = 0
-8a + 2af + -10a2 = 0 + 10a2 + -10a2
-8a + 2af + -10a2 = 10a2 + -10a2

Combine like terms: 10a2 + -10a2 = 0
-8a + 2af + -10a2 = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-4 + f + -5a) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-4 + f + -5a)' equal to zero and attempt to solve:

Simplifying
-4 + f + -5a = 0

Reorder the terms:
-4 + -5a + f = 0

Solving
-4 + -5a + f = 0

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

Add '4' to each side of the equation.
-4 + -5a + 4 + f = 0 + 4

Reorder the terms:
-4 + 4 + -5a + f = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5a + f = 0 + 4
-5a + f = 0 + 4

Combine like terms: 0 + 4 = 4
-5a + f = 4

Add '-1f' to each side of the equation.
-5a + f + -1f = 4 + -1f

Combine like terms: f + -1f = 0
-5a + 0 = 4 + -1f
-5a = 4 + -1f

Divide each side by '-5'.
a = -0.8 + 0.2f

Simplifying
a = -0.8 + 0.2f
Solution
a = {0, -0.8 + 0.2f}