f(2a)=a(a+3)

Solution for f(2a)=a(a+3) equation:

Simplifying
f(2a) = a(a + 3)

Remove parenthesis around (2a)
f * 2a = a(a + 3)

Reorder the terms for easier multiplication:
2f * a = a(a + 3)

Multiply f * a
2af = a(a + 3)

Reorder the terms:
2af = a(3 + a)
2af = (3 * a + a * a)
2af = (3a + a2)

Solving
2af = 3a + a2

Solving for variable 'a'.

Reorder the terms:
-3a + 2af + -1a2 = 3a + a2 + -3a + -1a2

Reorder the terms:
-3a + 2af + -1a2 = 3a + -3a + a2 + -1a2

Combine like terms: 3a + -3a = 0
-3a + 2af + -1a2 = 0 + a2 + -1a2
-3a + 2af + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-3a + 2af + -1a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-3 + 2f + -1a) = 0

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 '(-3 + 2f + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + 2f + -1a = 0

Reorder the terms:
-3 + -1a + 2f = 0

Solving
-3 + -1a + 2f = 0

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

Add '3' to each side of the equation.
-3 + -1a + 3 + 2f = 0 + 3

Reorder the terms:
-3 + 3 + -1a + 2f = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a + 2f = 0 + 3
-1a + 2f = 0 + 3

Combine like terms: 0 + 3 = 3
-1a + 2f = 3

Add '-2f' to each side of the equation.
-1a + 2f + -2f = 3 + -2f

Combine like terms: 2f + -2f = 0
-1a + 0 = 3 + -2f
-1a = 3 + -2f

Divide each side by '-1'.
a = -3 + 2f

Simplifying
a = -3 + 2f
Solution
a = {0, -3 + 2f}