Solve for a 5(14/5a-6)+8(3/4a-3)=2a

$5 (\frac{14}{5} a - 6) + 8 (\frac{3}{4} a - 3) = 2 a$

Step 1

Simplify $5 (\frac{14}{5} a - 6) + 8 (\frac{3}{4} a - 3)$ .

Simplify each term.

Combine $\frac{14}{5}$ and $a$ .

$5 (\frac{14 a}{5} - 6) + 8 (\frac{3}{4} a - 3) = 2 a$

Apply the distributive property.

$5 \frac{14 a}{5} + 5 \cdot - 6 + 8 (\frac{3}{4} a - 3) = 2 a$

Cancel the common factor of $5$ .

Cancel the common factor.

$5 \frac{14 a}{5} + 5 \cdot - 6 + 8 (\frac{3}{4} a - 3) = 2 a$

Rewrite the expression.

$14 a + 5 \cdot - 6 + 8 (\frac{3}{4} a - 3) = 2 a$

Multiply $5$ by $- 6$ .

$14 a - 30 + 8 (\frac{3}{4} a - 3) = 2 a$

Combine $\frac{3}{4}$ and $a$ .

$14 a - 30 + 8 (\frac{3 a}{4} - 3) = 2 a$

Apply the distributive property.

$14 a - 30 + 8 \frac{3 a}{4} + 8 \cdot - 3 = 2 a$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$14 a - 30 + 4 (2) \frac{3 a}{4} + 8 \cdot - 3 = 2 a$

Cancel the common factor.

$14 a - 30 + 4 \cdot 2 \frac{3 a}{4} + 8 \cdot - 3 = 2 a$

Rewrite the expression.

$14 a - 30 + 2 (3 a) + 8 \cdot - 3 = 2 a$

Multiply $3$ by $2$ .

$14 a - 30 + 6 a + 8 \cdot - 3 = 2 a$

Multiply $8$ by $- 3$ .

$14 a - 30 + 6 a - 24 = 2 a$

Simplify by adding terms.

Add $14 a$ and $6 a$ .

$20 a - 30 - 24 = 2 a$

Subtract $24$ from $- 30$ .

$20 a - 54 = 2 a$

Step 2

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

Subtract $2 a$ from both sides of the equation.

$20 a - 54 - 2 a = 0$

Subtract $2 a$ from $20 a$ .

$18 a - 54 = 0$

Step 3

Add $54$ to both sides of the equation.

$18 a = 54$

Step 4

Divide each term in $18 a = 54$ by $18$ and simplify.

Divide each term in $18 a = 54$ by $18$ .

$\frac{18 a}{18} = \frac{54}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 a}{18} = \frac{54}{18}$

Divide $a$ by $1$ .

$a = \frac{54}{18}$

Simplify the right side.

Divide $54$ by $18$ .

$a = 3$

Solve for a 5(14/5a-6)+8(3/4a-3)=2a

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