=4[f(0)+f(4)+f(8)+f(12)+f(16)]

Solution for =4[f(0)+f(4)+f(8)+f(12)+f(16)] equation:

Simplifying
0 = 4[f(0) + f(4) + f(8) + f(12) + f(16)]

Reorder the terms for easier multiplication:
0 = 4[0f + f(4) + f(8) + f(12) + f(16)]

Anything times zero is zero.
0 = 4[0f + f(4) + f(8) + f(12) + f(16)]

Reorder the terms for easier multiplication:
0 = 4[0 + 4f + f(8) + f(12) + f(16)]

Reorder the terms for easier multiplication:
0 = 4[0 + 4f + 8f + f(12) + f(16)]

Reorder the terms for easier multiplication:
0 = 4[0 + 4f + 8f + 12f + f(16)]

Reorder the terms for easier multiplication:
0 = 4[0 + 4f + 8f + 12f + 16f]
Remove the zero:
0 = 4[4f + 8f + 12f + 16f]

Combine like terms: 4f + 8f = 12f
0 = 4[12f + 12f + 16f]

Combine like terms: 12f + 12f = 24f
0 = 4[24f + 16f]

Combine like terms: 24f + 16f = 40f
0 = 4[40f]

Remove brackets around [40f]
0 = 4 * 40f

Multiply 4 * 40
0 = 160f

Solving
0 = 160f

Solving for variable 'f'.

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

Add '-160f' to each side of the equation.
0 + -160f = 160f + -160f
Remove the zero:
-160f = 160f + -160f

Combine like terms: 160f + -160f = 0
-160f = 0

Divide each side by '-160'.
f = 0

Simplifying
f = 0