Solve for c 25c+10c^2=0

$25 c + 10 c^{2} = 0$

Factor the left side of the equation.

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

$25 u + 10 u^{2} = 0$

Factor $5 u$ out of $25 u + 10 u^{2}$ .

Factor $5 u$ out of $25 u$ .

$5 u (5) + 10 u^{2} = 0$

Factor $5 u$ out of $10 u^{2}$ .

$5 u (5) + 5 u (2 u) = 0$

Factor $5 u$ out of $5 u (5) + 5 u (2 u)$ .

$5 u (5 + 2 u) = 0$

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

$5 c (5 + 2 c) = 0$

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

$c = 0$

$5 + 2 c = 0$

Set $c$ equal to $0$ .

$c = 0$

Set $5 + 2 c$ equal to $0$ and solve for $c$ .

Set $5 + 2 c$ equal to $0$ .

$5 + 2 c = 0$

Solve $5 + 2 c = 0$ for $c$ .

Subtract $5$ from both sides of the equation.

$2 c = - 5$

Divide each term in $2 c = - 5$ by $2$ and simplify.

Divide each term in $2 c = - 5$ by $2$ .

$\frac{2 c}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 c}{2} = \frac{- 5}{2}$

Divide $c$ by $1$ .

$c = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$c = - \frac{5}{2}$

The final solution is all the values that make $5 c (5 + 2 c) = 0$ true.

$c = 0, - \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$c = 0, - \frac{5}{2}$

Decimal Form:

$c = 0, - 2.5$

Mixed Number Form:

$c = 0, - 2 \frac{1}{2}$