Solve for f 4+10f=7(2f-4)

$4 + 10 f = 7 (2 f - 4)$

Step 1

Simplify $7 (2 f - 4)$ .

Rewrite.

$4 + 10 f = 0 + 0 + 7 (2 f - 4)$

Simplify by adding zeros.

$4 + 10 f = 7 (2 f - 4)$

Apply the distributive property.

$4 + 10 f = 7 (2 f) + 7 \cdot - 4$

Multiply.

Multiply $2$ by $7$ .

$4 + 10 f = 14 f + 7 \cdot - 4$

Multiply $7$ by $- 4$ .

$4 + 10 f = 14 f - 28$

Step 2

Move all terms containing $f$ to the left side of the equation.

Subtract $14 f$ from both sides of the equation.

$4 + 10 f - 14 f = - 28$

Subtract $14 f$ from $10 f$ .

$4 - 4 f = - 28$

Step 3

Move all terms not containing $f$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- 4 f = - 28 - 4$

Subtract $4$ from $- 28$ .

$- 4 f = - 32$

Step 4

Divide each term in $- 4 f = - 32$ by $- 4$ and simplify.

Divide each term in $- 4 f = - 32$ by $- 4$ .

$\frac{- 4 f}{- 4} = \frac{- 32}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 f}{- 4} = \frac{- 32}{- 4}$

Divide $f$ by $1$ .

$f = \frac{- 32}{- 4}$

Simplify the right side.

Divide $- 32$ by $- 4$ .

$f = 8$