Algebra Examples

$y = {(x - 1)}^{2} {(2 x - 3)}^{3}$

Step 1

Set ${(x - 1)}^{2} {(2 x - 3)}^{3}$ equal to $0$ .

${(x - 1)}^{2} {(2 x - 3)}^{3} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

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

${(x - 1)}^{2} = 0$

${(2 x - 3)}^{3} = 0$

Step 2.2

Set ${(x - 1)}^{2}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.2.1

Set ${(x - 1)}^{2}$ equal to $0$ .

${(x - 1)}^{2} = 0$

Step 2.2.2

Solve ${(x - 1)}^{2} = 0$ for $x$ .

Tap for more steps...

Step 2.2.2.1

Set the $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 2.2.2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 2.3

Set ${(2 x - 3)}^{3}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set ${(2 x - 3)}^{3}$ equal to $0$ .

${(2 x - 3)}^{3} = 0$

Step 2.3.2

Solve ${(2 x - 3)}^{3} = 0$ for $x$ .

Tap for more steps...

Step 2.3.2.1

Set the $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Step 2.3.2.2

Solve for $x$ .

Tap for more steps...

Step 2.3.2.2.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 2.3.2.2.2

Divide each term in $2 x = 3$ by $2$ and simplify.

Tap for more steps...

Step 2.3.2.2.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 2.3.2.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.2.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 2.3.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 2.4

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

$x = 1, \frac{3}{2}$

Step 3