Solve by Factoring 2(a-8)+7=5(a+2)-3a-19

$2 (a - 8) + 7 = 5 (a + 2) - 3 a - 19$

Step 1

Move all the expressions to the left side of the equation.

Subtract $5 (a + 2)$ from both sides of the equation.

$2 (a - 8) + 7 - 5 (a + 2) = - 3 a - 19$

Add $3 a$ to both sides of the equation.

$2 (a - 8) + 7 - 5 (a + 2) + 3 a = - 19$

Add $19$ to both sides of the equation.

$2 (a - 8) + 7 - 5 (a + 2) + 3 a + 19 = 0$

Step 2

Simplify $2 (a - 8) + 7 - 5 (a + 2) + 3 a + 19$ .

Simplify each term.

Apply the distributive property.

$2 a + 2 \cdot - 8 + 7 - 5 (a + 2) + 3 a + 19 = 0$

Multiply $2$ by $- 8$ .

$2 a - 16 + 7 - 5 (a + 2) + 3 a + 19 = 0$

Apply the distributive property.

$2 a - 16 + 7 - 5 a - 5 \cdot 2 + 3 a + 19 = 0$

Multiply $- 5$ by $2$ .

$2 a - 16 + 7 - 5 a - 10 + 3 a + 19 = 0$

Subtract $5 a$ from $2 a$ .

$- 3 a - 16 + 7 - 10 + 3 a + 19 = 0$

Combine the opposite terms in $- 3 a - 16 + 7 - 10 + 3 a + 19$ .

Add $- 3 a$ and $3 a$ .

$0 - 16 + 7 - 10 + 19 = 0$

Subtract $16$ from $0$ .

$- 16 + 7 - 10 + 19 = 0$

Add $- 16$ and $7$ .

$- 9 - 10 + 19 = 0$

Subtract $10$ from $- 9$ .

$- 19 + 19 = 0$

Add $- 19$ and $19$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true