Solve for x 3x=0.5x^2

$3 x = 0.5 x^{2}$

Step 1

Subtract $0.5 x^{2}$ from both sides of the equation.

$3 x - 0.5 x^{2} = 0$

Step 2

Factor the left side of the equation.

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

$3 u - 0.5 u^{2} = 0$

Factor $0.5 u$ out of $3 u - 0.5 u^{2}$ .

Factor $0.5 u$ out of $3 u$ .

$0.5 u (6) - 0.5 u^{2} = 0$

Factor $0.5 u$ out of $- 0.5 u^{2}$ .

$0.5 u (6) + 0.5 u (- u) = 0$

Factor $0.5 u$ out of $0.5 u (6) + 0.5 u (- u)$ .

$0.5 u (6 - u) = 0$

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

$0.5 x (6 - x) = 0$

Step 3

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

$x = 0$

$6 - x = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $6 - x$ equal to $0$ and solve for $x$ .

Set $6 - x$ equal to $0$ .

$6 - x = 0$

Solve $6 - x = 0$ for $x$ .

Subtract $6$ from both sides of the equation.

$- x = - 6$

Divide each term in $- x = - 6$ by $- 1$ and simplify.

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x = 6$

Step 6

The final solution is all the values that make $0.5 x (6 - x) = 0$ true.

$x = 0, 6$