2(2f+3)+3(4f-1)-2(5f+3)=0

Solution for 2(2f+3)+3(4f-1)-2(5f+3)=0 equation:

Simplifying
2(2f + 3) + 3(4f + -1) + -2(5f + 3) = 0

Reorder the terms:
2(3 + 2f) + 3(4f + -1) + -2(5f + 3) = 0
(3 * 2 + 2f * 2) + 3(4f + -1) + -2(5f + 3) = 0
(6 + 4f) + 3(4f + -1) + -2(5f + 3) = 0

Reorder the terms:
6 + 4f + 3(-1 + 4f) + -2(5f + 3) = 0
6 + 4f + (-1 * 3 + 4f * 3) + -2(5f + 3) = 0
6 + 4f + (-3 + 12f) + -2(5f + 3) = 0

Reorder the terms:
6 + 4f + -3 + 12f + -2(3 + 5f) = 0
6 + 4f + -3 + 12f + (3 * -2 + 5f * -2) = 0
6 + 4f + -3 + 12f + (-6 + -10f) = 0

Reorder the terms:
6 + -3 + -6 + 4f + 12f + -10f = 0

Combine like terms: 6 + -3 = 3
3 + -6 + 4f + 12f + -10f = 0

Combine like terms: 3 + -6 = -3
-3 + 4f + 12f + -10f = 0

Combine like terms: 4f + 12f = 16f
-3 + 16f + -10f = 0

Combine like terms: 16f + -10f = 6f
-3 + 6f = 0

Solving
-3 + 6f = 0

Solving for variable 'f'.

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

Add '3' to each side of the equation.
-3 + 3 + 6f = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6f = 0 + 3
6f = 0 + 3

Combine like terms: 0 + 3 = 3
6f = 3

Divide each side by '6'.
f = 0.5

Simplifying
f = 0.5