Precalculus Examples

$5 y (3 - y) {(4 y + 1)}^{2} = 0$

Step 1

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

$y = 0$

$3 - y = 0$

${(4 y + 1)}^{2} = 0$

Step 2

Set $y$ equal to $0$ .

$y = 0$

Step 3

Set $3 - y$ equal to $0$ and solve for $y$ .

Tap for more steps...

Step 3.1

Set $3 - y$ equal to $0$ .

$3 - y = 0$

Step 3.2

Solve $3 - y = 0$ for $y$ .

Tap for more steps...

Step 3.2.1

Subtract $3$ from both sides of the equation.

$- y = - 3$

Step 3.2.2

Divide each term in $- y = - 3$ by $- 1$ and simplify.

Tap for more steps...

Step 3.2.2.1

Divide each term in $- y = - 3$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 3}{- 1}$

Step 3.2.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 3}{- 1}$

Step 3.2.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 3}{- 1}$

Step 3.2.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.2.3.1

Divide $- 3$ by $- 1$ .

$y = 3$

Step 4

Set ${(4 y + 1)}^{2}$ equal to $0$ and solve for $y$ .

Tap for more steps...

Step 4.1

Set ${(4 y + 1)}^{2}$ equal to $0$ .

${(4 y + 1)}^{2} = 0$

Step 4.2

Solve ${(4 y + 1)}^{2} = 0$ for $y$ .

Tap for more steps...

Step 4.2.1

Set the $4 y + 1$ equal to $0$ .

$4 y + 1 = 0$

Step 4.2.2

Solve for $y$ .

Tap for more steps...

Step 4.2.2.1

Subtract $1$ from both sides of the equation.

$4 y = - 1$

Step 4.2.2.2

Divide each term in $4 y = - 1$ by $4$ and simplify.

Tap for more steps...

Step 4.2.2.2.1

Divide each term in $4 y = - 1$ by $4$ .

$\frac{4 y}{4} = \frac{- 1}{4}$

Step 4.2.2.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.2.2.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 1}{4}$

Step 4.2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1}{4}$

Step 4.2.2.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.2.2.3.1

Move the negative in front of the fraction.

$y = - \frac{1}{4}$

Step 5

The final solution is all the values that make $5 y (3 - y) {(4 y + 1)}^{2} = 0$ true.

$y = 0, 3, - \frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = 0, 3, - \frac{1}{4}$

Decimal Form:

$y = 0, 3, - 0.25$