Solve for a 7a-14a^2=0

$7 a - 14 a^{2} = 0$

Factor the left side of the equation.

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

$7 u - 14 u^{2} = 0$

Factor $7 u$ out of $7 u - 14 u^{2}$ .

Factor $7 u$ out of $7 u$ .

$7 u (1) - 14 u^{2} = 0$

Factor $7 u$ out of $- 14 u^{2}$ .

$7 u (1) + 7 u (- 2 u) = 0$

Factor $7 u$ out of $7 u (1) + 7 u (- 2 u)$ .

$7 u (1 - 2 u) = 0$

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

$7 a (1 - 2 a) = 0$

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

$a = 0$

$1 - 2 a = 0$

Set $a$ equal to $0$ .

$a = 0$

Set $1 - 2 a$ equal to $0$ and solve for $a$ .

Set $1 - 2 a$ equal to $0$ .

$1 - 2 a = 0$

Solve $1 - 2 a = 0$ for $a$ .

Subtract $1$ from both sides of the equation.

$- 2 a = - 1$

Divide each term in $- 2 a = - 1$ by $- 2$ and simplify.

Divide each term in $- 2 a = - 1$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{- 1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 1}{- 2}$

Divide $a$ by $1$ .

$a = \frac{- 1}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$a = \frac{1}{2}$

The final solution is all the values that make $7 a (1 - 2 a) = 0$ true.

$a = 0, \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$a = 0, \frac{1}{2}$

Decimal Form:

$a = 0, 0.5$