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

$(3 x - 4) (x + 5)$

Write $(3 x - 4) (x + 5)$ as an equation.

$y = (3 x - 4) (x + 5)$

Find the x-intercepts.

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

$0 = (3 x - 4) (x + 5)$

Solve the equation.

Rewrite the equation as $(3 x - 4) (x + 5) = 0$ .

$(3 x - 4) (x + 5) = 0$

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

$3 x - 4 = 0$

$x + 5 = 0$

Set $3 x - 4$ equal to $0$ and solve for $x$ .

Set $3 x - 4$ equal to $0$ .

$3 x - 4 = 0$

Solve $3 x - 4 = 0$ for $x$ .

Add $4$ to both sides of the equation.

$3 x = 4$

Divide each term in $3 x = 4$ by $3$ and simplify.

Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Divide $x$ by $1$ .

$x = \frac{4}{3}$

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

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

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $(3 x - 4) (x + 5) = 0$ true.

$x = \frac{4}{3}, - 5$

x-intercept(s) in point form.

x-intercept(s): $(\frac{4}{3}, 0), (- 5, 0)$

Find the y-intercepts.

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

$y = (3 (0) - 4) ((0) + 5)$

Solve the equation.

Remove parentheses.

$y = (3 (0) - 4) (0 + 5)$

Remove parentheses.

$y = (3 (0) - 4) ((0) + 5)$

Simplify $(3 (0) - 4) ((0) + 5)$ .

Multiply $3$ by $0$ .

$y = (0 - 4) ((0) + 5)$

Subtract $4$ from $0$ .

$y = - 4 ((0) + 5)$

Add $0$ and $5$ .

$y = - 4 \cdot 5$

Multiply $- 4$ by $5$ .

$y = - 20$

y-intercept(s) in point form.

y-intercept(s): $(0, - 20)$

List the intersections.

x-intercept(s): $(\frac{4}{3}, 0), (- 5, 0)$

y-intercept(s): $(0, - 20)$

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

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