Algebra Examples

$\frac{1}{4} y^{2} + y = 0$

Step 1

Combine $\frac{1}{4}$ and $y^{2}$ .

$\frac{y^{2}}{4} + y = 0$

Step 2

Multiply each term in $\frac{y^{2}}{4} + y = 0$ by $4$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{y^{2}}{4} + y = 0$ by $4$ .

$\frac{y^{2}}{4} \cdot 4 + y \cdot 4 = 0 \cdot 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Cancel the common factor.

$\frac{y^{2}}{4} \cdot 4 + y \cdot 4 = 0 \cdot 4$

Step 2.2.1.1.2

Rewrite the expression.

$y^{2} + y \cdot 4 = 0 \cdot 4$

Step 2.2.1.2

Move $4$ to the left of $y$ .

$y^{2} + 4 y = 0 \cdot 4$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $0$ by $4$ .

$y^{2} + 4 y = 0$

Step 3

Factor $y$ out of $y^{2} + 4 y$ .

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Step 3.1

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

$y \cdot y + 4 y = 0$

Step 3.2

Factor $y$ out of $4 y$ .

$y \cdot y + y \cdot 4 = 0$

Step 3.3

Factor $y$ out of $y \cdot y + y \cdot 4$ .

$y (y + 4) = 0$

Step 4

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

$y = 0$

$y + 4 = 0$

Step 5

Set $y$ equal to $0$ .

$y = 0$

Step 6

Set $y + 4$ equal to $0$ and solve for $y$ .

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Step 6.1

Set $y + 4$ equal to $0$ .

$y + 4 = 0$

Step 6.2

Subtract $4$ from both sides of the equation.

$y = - 4$

Step 7

The final solution is all the values that make $y (y + 4) = 0$ true.

$y = 0, - 4$