Finite Math Examples

$3 x = 6 x^{2}$

Step 1

Subtract $6 x^{2}$ from both sides of the equation.

$3 x - 6 x^{2} = 0$

Step 2

Factor the left side of the equation.

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Step 2.1

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

$3 u - 6 u^{2} = 0$

Step 2.2

Factor $3 u$ out of $3 u - 6 u^{2}$ .

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Step 2.2.1

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

$3 u (1) - 6 u^{2} = 0$

Step 2.2.2

Factor $3 u$ out of $- 6 u^{2}$ .

$3 u (1) + 3 u (- 2 u) = 0$

Step 2.2.3

Factor $3 u$ out of $3 u (1) + 3 u (- 2 u)$ .

$3 u (1 - 2 u) = 0$

Step 2.3

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

$3 x (1 - 2 x) = 0$

Step 3

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

$x = 0$

$1 - 2 x = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

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

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Step 5.1

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

$1 - 2 x = 0$

Step 5.2

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

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Step 5.2.1

Subtract $1$ from both sides of the equation.

$- 2 x = - 1$

Step 5.2.2

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

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Step 5.2.2.1

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

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

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

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

Step 5.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 5.2.2.3

Simplify the right side.

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Step 5.2.2.3.1

Dividing two negative values results in a positive value.

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

Step 6

The final solution is all the values that make $3 x (1 - 2 x) = 0$ true.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0, 0.5$