Finite Math Examples

$5 x^{2} - 16 x = 0$

Step 1

Factor $x$ out of $5 x^{2} - 16 x$ .

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Step 1.1

Factor $x$ out of $5 x^{2}$ .

$x (5 x) - 16 x = 0$

Step 1.2

Factor $x$ out of $- 16 x$ .

$x (5 x) + x \cdot - 16 = 0$

Step 1.3

Factor $x$ out of $x (5 x) + x \cdot - 16$ .

$x (5 x - 16) = 0$

Step 2

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

$x = 0$

$5 x - 16 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $5 x - 16$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $5 x - 16$ equal to $0$ .

$5 x - 16 = 0$

Step 4.2

Solve $5 x - 16 = 0$ for $x$ .

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Step 4.2.1

Add $16$ to both sides of the equation.

$5 x = 16$

Step 4.2.2

Divide each term in $5 x = 16$ by $5$ and simplify.

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Step 4.2.2.1

Divide each term in $5 x = 16$ by $5$ .

$\frac{5 x}{5} = \frac{16}{5}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{16}{5}$

Step 4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{5}$

Step 5

The final solution is all the values that make $x (5 x - 16) = 0$ true.

$x = 0, \frac{16}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{16}{5}$

Decimal Form:

$x = 0, 3.2$

Mixed Number Form:

$x = 0, 3 \frac{1}{5}$