Solve for f -45=-6(-4+3f)

$- 45 = - 6 (- 4 + 3 f)$

Step 1

Rewrite the equation as $- 6 (- 4 + 3 f) = - 45$ .

$- 6 (- 4 + 3 f) = - 45$

Step 2

Divide each term in $- 6 (- 4 + 3 f) = - 45$ by $- 6$ and simplify.

Divide each term in $- 6 (- 4 + 3 f) = - 45$ by $- 6$ .

$\frac{- 6 (- 4 + 3 f)}{- 6} = \frac{- 45}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 (- 4 + 3 f)}{- 6} = \frac{- 45}{- 6}$

Divide $- 4 + 3 f$ by $1$ .

$- 4 + 3 f = \frac{- 45}{- 6}$

Simplify the right side.

Cancel the common factor of $- 45$ and $- 6$ .

Factor $- 3$ out of $- 45$ .

$- 4 + 3 f = \frac{- 3 (15)}{- 6}$

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

$- 4 + 3 f = \frac{- 3 \cdot 15}{- 3 \cdot 2}$

Cancel the common factor.

$- 4 + 3 f = \frac{- 3 \cdot 15}{- 3 \cdot 2}$

Rewrite the expression.

$- 4 + 3 f = \frac{15}{2}$

Step 3

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

Add $4$ to both sides of the equation.

$3 f = \frac{15}{2} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 f = \frac{15}{2} + 4 \cdot \frac{2}{2}$

Combine $4$ and $\frac{2}{2}$ .

$3 f = \frac{15}{2} + \frac{4 \cdot 2}{2}$

Combine the numerators over the common denominator.

$3 f = \frac{15 + 4 \cdot 2}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$3 f = \frac{15 + 8}{2}$

Add $15$ and $8$ .

$3 f = \frac{23}{2}$

Step 4

Divide each term in $3 f = \frac{23}{2}$ by $3$ and simplify.

Divide each term in $3 f = \frac{23}{2}$ by $3$ .

$\frac{3 f}{3} = \frac{\frac{23}{2}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 f}{3} = \frac{\frac{23}{2}}{3}$

Divide $f$ by $1$ .

$f = \frac{\frac{23}{2}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{23}{2} \cdot \frac{1}{3}$

Multiply $\frac{23}{2} \cdot \frac{1}{3}$ .

Multiply $\frac{23}{2}$ by $\frac{1}{3}$ .

$f = \frac{23}{2 \cdot 3}$

Multiply $2$ by $3$ .

$f = \frac{23}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$f = \frac{23}{6}$

Decimal Form:

$f = 3.8\overline{3}$

Mixed Number Form:

$f = 3 \frac{5}{6}$

Solve for f -45=-6(-4+3f)

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