Find the x and y Intercepts f(x)=2x(x-5)(2x+3)

$f (x) = 2 x (x - 5) (2 x + 3)$

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 2 x (x - 5) (2 x + 3)$

Solve the equation.

Rewrite the equation as $2 x (x - 5) (2 x + 3) = 0$ .

$2 x (x - 5) (2 x + 3) = 0$

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

$x = 0$

$x - 5 = 0$

$2 x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Set $2 x + 3$ equal to $0$ and solve for $x$ .

Set $2 x + 3$ equal to $0$ .

$2 x + 3 = 0$

Solve $2 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$2 x = - 3$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The final solution is all the values that make $2 x (x - 5) (2 x + 3) = 0$ true.

$x = 0, 5, - \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (5, 0), (- \frac{3}{2}, 0)$

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 2 (0) ((0) - 5) (2 (0) + 3)$

Solve the equation.

Remove parentheses.

$y = 2 (0) (0 - 5) (2 (0) + 3)$

Remove parentheses.

$y = 2 (0) ((0) - 5) (2 (0) + 3)$

Simplify $2 (0) ((0) - 5) (2 (0) + 3)$ .

Multiply $2$ by $0$ .

$y = 0 ((0) - 5) (2 (0) + 3)$

Subtract $5$ from $0$ .

$y = 0 \cdot - 5 (2 (0) + 3)$

Multiply $0$ by $- 5$ .

$y = 0 (2 (0) + 3)$

Multiply $2$ by $0$ .

$y = 0 (0 + 3)$

Add $0$ and $3$ .

$y = 0 \cdot 3$

Multiply $0$ by $3$ .

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

List the intersections.

x-intercept(s): $(0, 0), (5, 0), (- \frac{3}{2}, 0)$

y-intercept(s): $(0, 0)$

Find the x and y Intercepts f(x)=2x(x-5)(2x+3)

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