Solve for a 4(2a-9)=5(3a-7)-1

$4 (2 a - 9) = 5 (3 a - 7) - 1$

Step 1

Simplify $4 (2 a - 9)$ .

Rewrite.

$0 + 0 + 4 (2 a - 9) = 5 (3 a - 7) - 1$

Simplify by adding zeros.

$4 (2 a - 9) = 5 (3 a - 7) - 1$

Apply the distributive property.

$4 (2 a) + 4 \cdot - 9 = 5 (3 a - 7) - 1$

Multiply.

Multiply $2$ by $4$ .

$8 a + 4 \cdot - 9 = 5 (3 a - 7) - 1$

Multiply $4$ by $- 9$ .

$8 a - 36 = 5 (3 a - 7) - 1$

Step 2

Simplify $5 (3 a - 7) - 1$ .

Simplify each term.

Apply the distributive property.

$8 a - 36 = 5 (3 a) + 5 \cdot - 7 - 1$

Multiply $3$ by $5$ .

$8 a - 36 = 15 a + 5 \cdot - 7 - 1$

Multiply $5$ by $- 7$ .

$8 a - 36 = 15 a - 35 - 1$

Subtract $1$ from $- 35$ .

$8 a - 36 = 15 a - 36$

Step 3

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

Subtract $15 a$ from both sides of the equation.

$8 a - 36 - 15 a = - 36$

Subtract $15 a$ from $8 a$ .

$- 7 a - 36 = - 36$

Step 4

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

Add $36$ to both sides of the equation.

$- 7 a = - 36 + 36$

Add $- 36$ and $36$ .

$- 7 a = 0$

Step 5

Divide each term in $- 7 a = 0$ by $- 7$ and simplify.

Divide each term in $- 7 a = 0$ by $- 7$ .

$\frac{- 7 a}{- 7} = \frac{0}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 a}{- 7} = \frac{0}{- 7}$

Divide $a$ by $1$ .

$a = \frac{0}{- 7}$

Simplify the right side.

Divide $0$ by $- 7$ .

$a = 0$

Solve for a 4(2a-9)=5(3a-7)-1

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