Algebra Examples

$6 y^{2} = - 30 y$

Step 1

Add $30 y$ to both sides of the equation.

$6 y^{2} + 30 y = 0$

Step 2

Factor $6 y$ out of $6 y^{2} + 30 y$ .

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Step 2.1

Factor $6 y$ out of $6 y^{2}$ .

$6 y (y) + 30 y = 0$

Step 2.2

Factor $6 y$ out of $30 y$ .

$6 y (y) + 6 y (5) = 0$

Step 2.3

Factor $6 y$ out of $6 y (y) + 6 y (5)$ .

$6 y (y + 5) = 0$

Step 3

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

$y = 0$

$y + 5 = 0$

Step 4

Set $y$ equal to $0$ .

$y = 0$

Step 5

Set $y + 5$ equal to $0$ and solve for $y$ .

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Step 5.1

Set $y + 5$ equal to $0$ .

$y + 5 = 0$

Step 5.2

Subtract $5$ from both sides of the equation.

$y = - 5$

Step 6

The final solution is all the values that make $6 y (y + 5) = 0$ true.

$y = 0, - 5$