Finite Math Examples

$f (a) = 3 x^{2} + 2 x$

Step 1

Set $3 x^{2} + 2 x$ equal to $0$ .

$3 x^{2} + 2 x = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor $x$ out of $3 x^{2} + 2 x$ .

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Step 2.1.1

Factor $x$ out of $3 x^{2}$ .

$x (3 x) + 2 x = 0$

Step 2.1.2

Factor $x$ out of $2 x$ .

$x (3 x) + x \cdot 2 = 0$

Step 2.1.3

Factor $x$ out of $x (3 x) + x \cdot 2$ .

$x (3 x + 2) = 0$

Step 2.2

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

$x = 0$

$3 x + 2 = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

Set $3 x + 2$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $3 x + 2$ equal to $0$ .

$3 x + 2 = 0$

Step 2.4.2

Solve $3 x + 2 = 0$ for $x$ .

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Step 2.4.2.1

Subtract $2$ from both sides of the equation.

$3 x = - 2$

Step 2.4.2.2

Divide each term in $3 x = - 2$ by $3$ and simplify.

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Step 2.4.2.2.1

Divide each term in $3 x = - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2}{3}$

Step 2.4.2.2.2

Simplify the left side.

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Step 2.4.2.2.2.1

Cancel the common factor of $3$ .

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Step 2.4.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2}{3}$

Step 2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{3}$

Step 2.4.2.2.3

Simplify the right side.

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Step 2.4.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 2.5

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

$x = 0, - \frac{2}{3}$

Step 3