Solve for h 14/5(10h+25)=-6h+30-2h

$\frac{14}{5} (10 h + 25) = - 6 h + 30 - 2 h$

Step 1

Since $h$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 6 h + 30 - 2 h = \frac{14}{5} \cdot (10 h + 25)$

Step 2

Subtract $2 h$ from $- 6 h$ .

$- 8 h + 30 = \frac{14}{5} \cdot (10 h + 25)$

Step 3

Simplify $\frac{14}{5} \cdot (10 h + 25)$ .

Apply the distributive property.

$- 8 h + 30 = \frac{14}{5} (10 h) + \frac{14}{5} \cdot 25$

Cancel the common factor of $5$ .

Factor $5$ out of $10 h$ .

$- 8 h + 30 = \frac{14}{5} (5 (2 h)) + \frac{14}{5} \cdot 25$

Cancel the common factor.

$- 8 h + 30 = \frac{14}{5} (5 (2 h)) + \frac{14}{5} \cdot 25$

Rewrite the expression.

$- 8 h + 30 = 14 (2 h) + \frac{14}{5} \cdot 25$

Multiply $2$ by $14$ .

$- 8 h + 30 = 28 h + \frac{14}{5} \cdot 25$

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$- 8 h + 30 = 28 h + \frac{14}{5} \cdot (5 (5))$

Cancel the common factor.

$- 8 h + 30 = 28 h + \frac{14}{5} \cdot (5 \cdot 5)$

Rewrite the expression.

$- 8 h + 30 = 28 h + 14 \cdot 5$

Multiply $14$ by $5$ .

$- 8 h + 30 = 28 h + 70$

Step 4

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

Subtract $28 h$ from both sides of the equation.

$- 8 h + 30 - 28 h = 70$

Subtract $28 h$ from $- 8 h$ .

$- 36 h + 30 = 70$

Step 5

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

Subtract $30$ from both sides of the equation.

$- 36 h = 70 - 30$

Subtract $30$ from $70$ .

$- 36 h = 40$

Step 6

Divide each term in $- 36 h = 40$ by $- 36$ and simplify.

Divide each term in $- 36 h = 40$ by $- 36$ .

$\frac{- 36 h}{- 36} = \frac{40}{- 36}$

Simplify the left side.

Cancel the common factor of $- 36$ .

Cancel the common factor.

$\frac{- 36 h}{- 36} = \frac{40}{- 36}$

Divide $h$ by $1$ .

$h = \frac{40}{- 36}$

Simplify the right side.

Cancel the common factor of $40$ and $- 36$ .

Factor $4$ out of $40$ .

$h = \frac{4 (10)}{- 36}$

Cancel the common factors.

Factor $4$ out of $- 36$ .

$h = \frac{4 \cdot 10}{4 \cdot - 9}$

Cancel the common factor.

$h = \frac{4 \cdot 10}{4 \cdot - 9}$

Rewrite the expression.

$h = \frac{10}{- 9}$

Move the negative in front of the fraction.

$h = - \frac{10}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$h = - \frac{10}{9}$

Decimal Form:

$h = - 1.\overline{1}$

Mixed Number Form:

$h = - 1 \frac{1}{9}$

Solve for h 14/5(10h+25)=-6h+30-2h

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