Basic Math Examples

$- 10 r s + 6 r = 7 s$

Step 1

Factor $2 r$ out of $- 10 r s + 6 r$ .

Tap for more steps...

Step 1.1

Factor $2 r$ out of $- 10 r s$ .

$2 r (- 5 s) + 6 r = 7 s$

Step 1.2

Factor $2 r$ out of $6 r$ .

$2 r (- 5 s) + 2 r (3) = 7 s$

Step 1.3

Factor $2 r$ out of $2 r (- 5 s) + 2 r (3)$ .

$2 r (- 5 s + 3) = 7 s$

Step 2

Divide each term in $2 r (- 5 s + 3) = 7 s$ by $2 (- 5 s + 3)$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $2 r (- 5 s + 3) = 7 s$ by $2 (- 5 s + 3)$ .

$\frac{2 r (- 5 s + 3)}{2 (- 5 s + 3)} = \frac{7 s}{2 (- 5 s + 3)}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{2 r (- 5 s + 3)}{2 (- 5 s + 3)} = \frac{7 s}{2 (- 5 s + 3)}$

Step 2.2.1.2

Rewrite the expression.

$\frac{r (- 5 s + 3)}{- 5 s + 3} = \frac{7 s}{2 (- 5 s + 3)}$

Step 2.2.2

Cancel the common factor of $- 5 s + 3$ .

Tap for more steps...

Step 2.2.2.1

Cancel the common factor.

$\frac{r (- 5 s + 3)}{- 5 s + 3} = \frac{7 s}{2 (- 5 s + 3)}$

Step 2.2.2.2

Divide $r$ by $1$ .

$r = \frac{7 s}{2 (- 5 s + 3)}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Factor $- 1$ out of $- 5 s$ .

$r = \frac{7 s}{2 (- (5 s) + 3)}$

Step 2.3.2

Rewrite $3$ as $- 1 (- 3)$ .

$r = \frac{7 s}{2 (- (5 s) - 1 (- 3))}$

Step 2.3.3

Factor $- 1$ out of $- (5 s) - 1 (- 3)$ .

$r = \frac{7 s}{2 (- (5 s - 3))}$

Step 2.3.4

Rewrite negatives.

Tap for more steps...

Step 2.3.4.1

Rewrite $- (5 s - 3)$ as $- 1 (5 s - 3)$ .

$r = \frac{7 s}{2 (- 1 (5 s - 3))}$

Step 2.3.4.2

Move the negative in front of the fraction.

$r = - \frac{7 s}{2 (5 s - 3)}$