3[3f+1]=7[2f+9]

Solution for 3[3f+1]=7[2f+9] equation:

Simplifying
3[3f + 1] = 7[2f + 9]

Reorder the terms:
3[1 + 3f] = 7[2f + 9]
[1 * 3 + 3f * 3] = 7[2f + 9]
[3 + 9f] = 7[2f + 9]

Reorder the terms:
3 + 9f = 7[9 + 2f]
3 + 9f = [9 * 7 + 2f * 7]
3 + 9f = [63 + 14f]

Solving
3 + 9f = 63 + 14f

Solving for variable 'f'.

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

Add '-14f' to each side of the equation.
3 + 9f + -14f = 63 + 14f + -14f

Combine like terms: 9f + -14f = -5f
3 + -5f = 63 + 14f + -14f

Combine like terms: 14f + -14f = 0
3 + -5f = 63 + 0
3 + -5f = 63

Add '-3' to each side of the equation.
3 + -3 + -5f = 63 + -3

Combine like terms: 3 + -3 = 0
0 + -5f = 63 + -3
-5f = 63 + -3

Combine like terms: 63 + -3 = 60
-5f = 60

Divide each side by '-5'.
f = -12

Simplifying
f = -12