Find the Roots (Zeros) f(x)=3(5x+3)(x+2)(7x-1)

$f (x) = 3 (5 x + 3) (x + 2) (7 x - 1)$

Step 1

Set $3 (5 x + 3) (x + 2) (7 x - 1)$ equal to $0$ .

$3 (5 x + 3) (x + 2) (7 x - 1) = 0$

Step 2

Solve for $x$ .

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

$5 x + 3 = 0$

$x + 2 = 0$

$7 x - 1 = 0$

Set $5 x + 3$ equal to $0$ and solve for $x$ .

Set $5 x + 3$ equal to $0$ .

$5 x + 3 = 0$

Solve $5 x + 3 = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $7 x - 1$ equal to $0$ and solve for $x$ .

Set $7 x - 1$ equal to $0$ .

$7 x - 1 = 0$

Solve $7 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$7 x = 1$

Divide each term in $7 x = 1$ by $7$ and simplify.

Divide each term in $7 x = 1$ by $7$ .

$\frac{7 x}{7} = \frac{1}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{1}{7}$

Divide $x$ by $1$ .

$x = \frac{1}{7}$

The final solution is all the values that make $3 (5 x + 3) (x + 2) (7 x - 1) = 0$ true.

$x = - \frac{3}{5}, - 2, \frac{1}{7}$

Step 3

Find the Roots (Zeros) f(x)=3(5x+3)(x+2)(7x-1)

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