Solve for r -28r=4r^2

$- 28 r = 4 r^{2}$

Step 1

Subtract $4 r^{2}$ from both sides of the equation.

$- 28 r - 4 r^{2} = 0$

Step 2

Factor the left side of the equation.

Let $u = r$ . Substitute $u$ for all occurrences of $r$ .

$- 28 u - 4 u^{2} = 0$

Factor $4 u$ out of $- 28 u - 4 u^{2}$ .

Factor $4 u$ out of $- 28 u$ .

$4 u (- 7) - 4 u^{2} = 0$

Factor $4 u$ out of $- 4 u^{2}$ .

$4 u (- 7) + 4 u (- u) = 0$

Factor $4 u$ out of $4 u (- 7) + 4 u (- u)$ .

$4 u (- 7 - u) = 0$

Replace all occurrences of $u$ with $r$ .

$4 r (- 7 - r) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$r = 0$

$- 7 - r = 0$

Step 4

Set $r$ equal to $0$ .

$r = 0$

Step 5

Set $- 7 - r$ equal to $0$ and solve for $r$ .

Set $- 7 - r$ equal to $0$ .

$- 7 - r = 0$

Solve $- 7 - r = 0$ for $r$ .

Add $7$ to both sides of the equation.

$- r = 7$

Divide each term in $- r = 7$ by $- 1$ and simplify.

Divide each term in $- r = 7$ by $- 1$ .

$\frac{- r}{- 1} = \frac{7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{7}{- 1}$

Divide $r$ by $1$ .

$r = \frac{7}{- 1}$

Simplify the right side.

Divide $7$ by $- 1$ .

$r = - 7$

Step 6

The final solution is all the values that make $4 r (- 7 - r) = 0$ true.

$r = 0, - 7$