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

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$2 x - 3 = 0$

$5 x + 5 = 0$

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 $x$ .

Add $3$ to 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 $1$ .

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

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

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

$5 x + 5 = 0$

Solve $5 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$5 x = - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1$

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

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

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{2}, 0), (- 1, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

Multiply $2$ by $0$ .

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

Subtract $3$ from $0$ .

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

Multiply $2$ by $- 3$ .

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

Multiply $5$ by $0$ .

$y = - 6 (0 + 5)$

Add $0$ and $5$ .

$y = - 6 \cdot 5$

Multiply $- 6$ by $5$ .

$y = - 30$

y-intercept(s) in point form.

y-intercept(s): $(0, - 30)$

List the intersections.

x-intercept(s): $(\frac{3}{2}, 0), (- 1, 0)$

y-intercept(s): $(0, - 30)$

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

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