Basic Math Examples

$5 y^{2} - 2 y = 0$

Step 1

Factor $y$ out of $5 y^{2} - 2 y$ .

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Step 1.1

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

$y (5 y) - 2 y = 0$

Step 1.2

Factor $y$ out of $- 2 y$ .

$y (5 y) + y \cdot - 2 = 0$

Step 1.3

Factor $y$ out of $y (5 y) + y \cdot - 2$ .

$y (5 y - 2) = 0$

Step 2

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

$y = 0$

$5 y - 2 = 0$

Step 3

Set $y$ equal to $0$ .

$y = 0$

Step 4

Set $5 y - 2$ equal to $0$ and solve for $y$ .

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Step 4.1

Set $5 y - 2$ equal to $0$ .

$5 y - 2 = 0$

Step 4.2

Solve $5 y - 2 = 0$ for $y$ .

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Step 4.2.1

Add $2$ to both sides of the equation.

$5 y = 2$

Step 4.2.2

Divide each term in $5 y = 2$ by $5$ and simplify.

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Step 4.2.2.1

Divide each term in $5 y = 2$ by $5$ .

$\frac{5 y}{5} = \frac{2}{5}$

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.

$\frac{5 y}{5} = \frac{2}{5}$

Step 4.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{5}$

Step 5

The final solution is all the values that make $y (5 y - 2) = 0$ true.

$y = 0, \frac{2}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = 0, \frac{2}{5}$

Decimal Form:

$y = 0, 0.4$