2(f+5)+3(10-f)=6f-2

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Solution for 2(f+5)+3(10-f)=6f-2 equation: 


Simplifying
2(f + 5) + 3(10 + -1f) = 6f + -2

Reorder the terms:
2(5 + f) + 3(10 + -1f) = 6f + -2
(5 * 2 + f * 2) + 3(10 + -1f) = 6f + -2
(10 + 2f) + 3(10 + -1f) = 6f + -2
10 + 2f + (10 * 3 + -1f * 3) = 6f + -2
10 + 2f + (30 + -3f) = 6f + -2

Reorder the terms:
10 + 30 + 2f + -3f = 6f + -2

Combine like terms: 10 + 30 = 40
40 + 2f + -3f = 6f + -2

Combine like terms: 2f + -3f = -1f
40 + -1f = 6f + -2

Reorder the terms:
40 + -1f = -2 + 6f

Solving
40 + -1f = -2 + 6f

Solving for variable 'f'.

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

Add '-6f' to each side of the equation.
40 + -1f + -6f = -2 + 6f + -6f

Combine like terms: -1f + -6f = -7f
40 + -7f = -2 + 6f + -6f

Combine like terms: 6f + -6f = 0
40 + -7f = -2 + 0
40 + -7f = -2

Add '-40' to each side of the equation.
40 + -40 + -7f = -2 + -40

Combine like terms: 40 + -40 = 0
0 + -7f = -2 + -40
-7f = -2 + -40

Combine like terms: -2 + -40 = -42
-7f = -42

Divide each side by '-7'.
f = 6

Simplifying
f = 6

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