Find the x and y Intercepts f(x)=2x(5x-6)

$f (x) = 2 x (5 x - 6)$

Find the x-intercepts.

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

$0 = 2 x (5 x - 6)$

Solve the equation.

Rewrite the equation as $2 x (5 x - 6) = 0$ .

$2 x (5 x - 6) = 0$

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

$x = 0$

$5 x - 6 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $5 x - 6$ equal to $0$ and solve for $x$ .

Set $5 x - 6$ equal to $0$ .

$5 x - 6 = 0$

Solve $5 x - 6 = 0$ for $x$ .

Add $6$ to both sides of the equation.

$5 x = 6$

Divide each term in $5 x = 6$ by $5$ and simplify.

Divide each term in $5 x = 6$ by $5$ .

$\frac{5 x}{5} = \frac{6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{6}{5}$

Divide $x$ by $1$ .

$x = \frac{6}{5}$

The final solution is all the values that make $2 x (5 x - 6) = 0$ true.

$x = 0, \frac{6}{5}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\frac{6}{5}, 0)$

Find the y-intercepts.

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

$y = 2 (0) (5 (0) - 6)$

Solve the equation.

Remove parentheses.

$y = 2 (0) (5 (0) - 6)$

Simplify $2 (0) (5 (0) - 6)$ .

Multiply $2$ by $0$ .

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

Multiply $5$ by $0$ .

$y = 0 (0 - 6)$

Subtract $6$ from $0$ .

$y = 0 \cdot - 6$

Multiply $0$ by $- 6$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (\frac{6}{5}, 0)$

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

Find the x and y Intercepts f(x)=2x(5x-6)

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