Find the x and y Intercepts y=((x-4)(2x+3))/((3x+5)(x-2))

$y = \frac{(x - 4) (2 x + 3)}{(3 x + 5) (x - 2)}$

Find the x-intercepts.

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

$0 = \frac{(x - 4) (2 x + 3)}{(3 x + 5) (x - 2)}$

Solve the equation.

Set the numerator equal to zero.

$(x - 4) (2 x + 3) = 0$

Solve the equation for $x$ .

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

$x - 4 = 0$

$2 x + 3 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

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 $(x - 4) (2 x + 3) = 0$ true.

$x = 4, - \frac{3}{2}$

x-intercept(s) in point form.

x-intercept(s): $(4, 0), (- \frac{3}{2}, 0)$

Find the y-intercepts.

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

$y = \frac{((0) - 4) (2 (0) + 3)}{(3 (0) + 5) ((0) - 2)}$

Solve the equation.

Remove parentheses.

$y = \frac{(0 - 4) (2 (0) + 3)}{(3 (0) + 5) ((0) - 2)}$

Remove parentheses.

$y = \frac{(0 - 4) (2 (0) + 3)}{(3 (0) + 5) (0 - 2)}$

Remove parentheses.

$y = \frac{((0) - 4) (2 (0) + 3)}{(3 (0) + 5) ((0) - 2)}$

Simplify $\frac{((0) - 4) (2 (0) + 3)}{(3 (0) + 5) ((0) - 2)}$ .

Cancel the common factor of $(0) - 4$ and $(0) - 2$ .

Factor $2$ out of $((0) - 4) (2 (0) + 3)$ .

$y = \frac{2 ((0 - 2) (2 (0) + 3))}{(3 (0) + 5) ((0) - 2)}$

Cancel the common factors.

Factor $2$ out of $(3 (0) + 5) ((0) - 2)$ .

$y = \frac{2 ((0 - 2) (2 (0) + 3))}{2 ((3 (0) + 5) (0 - 1))}$

Cancel the common factor.

$y = \frac{2 ((0 - 2) (2 (0) + 3))}{2 ((3 (0) + 5) (0 - 1))}$

Rewrite the expression.

$y = \frac{(0 - 2) (2 (0) + 3)}{(3 (0) + 5) (0 - 1)}$

Simplify the numerator.

Subtract $2$ from $0$ .

$y = \frac{- 2 (2 (0) + 3)}{(3 (0) + 5) (0 - 1)}$

Multiply $2$ by $0$ .

$y = \frac{- 2 (0 + 3)}{(3 (0) + 5) (0 - 1)}$

Add $0$ and $3$ .

$y = \frac{- 2 \cdot 3}{(3 (0) + 5) (0 - 1)}$

Simplify the denominator.

Multiply $3$ by $0$ .

$y = \frac{- 2 \cdot 3}{(0 + 5) (0 - 1)}$

Add $0$ and $5$ .

$y = \frac{- 2 \cdot 3}{5 (0 - 1)}$

Subtract $1$ from $0$ .

$y = \frac{- 2 \cdot 3}{5 \cdot - 1}$

Reduce the expression by cancelling the common factors.

Multiply $- 2$ by $3$ .

$y = \frac{- 6}{5 \cdot - 1}$

Multiply $5$ by $- 1$ .

$y = \frac{- 6}{- 5}$

Dividing two negative values results in a positive value.

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

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(4, 0), (- \frac{3}{2}, 0)$

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

Find the x and y Intercepts y=((x-4)(2x+3))/((3x+5)(x-2))

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