Solve by Factoring 73=-6(k-7)+6(k+5)

$73 = - 6 (k - 7) + 6 (k + 5)$

Step 1

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

Add $6 (k - 7)$ to both sides of the equation.

$73 + 6 (k - 7) = 6 (k + 5)$

Subtract $6 (k + 5)$ from both sides of the equation.

$73 + 6 (k - 7) - 6 (k + 5) = 0$

Step 2

Simplify $73 + 6 (k - 7) - 6 (k + 5)$ .

Simplify each term.

Apply the distributive property.

$73 + 6 k + 6 \cdot - 7 - 6 (k + 5) = 0$

Multiply $6$ by $- 7$ .

$73 + 6 k - 42 - 6 (k + 5) = 0$

Apply the distributive property.

$73 + 6 k - 42 - 6 k - 6 \cdot 5 = 0$

Multiply $- 6$ by $5$ .

$73 + 6 k - 42 - 6 k - 30 = 0$

Combine the opposite terms in $73 + 6 k - 42 - 6 k - 30$ .

Subtract $6 k$ from $6 k$ .

$73 + 0 - 42 - 30 = 0$

Add $73$ and $0$ .

$73 - 42 - 30 = 0$

Subtract $42$ from $73$ .

$31 - 30 = 0$

Subtract $30$ from $31$ .

$1 = 0$

Step 3

Since $1 \neq 0$ , there are no solutions.

No solution