Solve for a -4/7(-56a+21)=-8a+5

$- \frac{4}{7} (- 56 a + 21) = - 8 a + 5$

Step 1

Simplify $- \frac{4}{7} \cdot (- 56 a + 21)$ .

Rewrite.

$0 + 0 - \frac{4}{7} \cdot (- 56 a + 21) = - 8 a + 5$

Simplify by adding zeros.

$- \frac{4}{7} \cdot (- 56 a + 21) = - 8 a + 5$

Apply the distributive property.

$- \frac{4}{7} (- 56 a) - \frac{4}{7} \cdot 21 = - 8 a + 5$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$\frac{- 4}{7} (- 56 a) - \frac{4}{7} \cdot 21 = - 8 a + 5$

Factor $7$ out of $- 56 a$ .

$\frac{- 4}{7} (7 (- 8 a)) - \frac{4}{7} \cdot 21 = - 8 a + 5$

Cancel the common factor.

$\frac{- 4}{7} (7 (- 8 a)) - \frac{4}{7} \cdot 21 = - 8 a + 5$

Rewrite the expression.

$- 4 (- 8 a) - \frac{4}{7} \cdot 21 = - 8 a + 5$

Multiply $- 8$ by $- 4$ .

$32 a - \frac{4}{7} \cdot 21 = - 8 a + 5$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{4}{7}$ into the numerator.

$32 a + \frac{- 4}{7} \cdot 21 = - 8 a + 5$

Factor $7$ out of $21$ .

$32 a + \frac{- 4}{7} \cdot (7 (3)) = - 8 a + 5$

Cancel the common factor.

$32 a + \frac{- 4}{7} \cdot (7 \cdot 3) = - 8 a + 5$

Rewrite the expression.

$32 a - 4 \cdot 3 = - 8 a + 5$

Multiply $- 4$ by $3$ .

$32 a - 12 = - 8 a + 5$

Step 2

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

Add $8 a$ to both sides of the equation.

$32 a - 12 + 8 a = 5$

Add $32 a$ and $8 a$ .

$40 a - 12 = 5$

Step 3

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

Add $12$ to both sides of the equation.

$40 a = 5 + 12$

Add $5$ and $12$ .

$40 a = 17$

Step 4

Divide each term in $40 a = 17$ by $40$ and simplify.

Divide each term in $40 a = 17$ by $40$ .

$\frac{40 a}{40} = \frac{17}{40}$

Simplify the left side.

Cancel the common factor of $40$ .

Cancel the common factor.

$\frac{40 a}{40} = \frac{17}{40}$

Divide $a$ by $1$ .

$a = \frac{17}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{17}{40}$

Decimal Form:

$a = 0.425$

Solve for a -4/7(-56a+21)=-8a+5

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