Solve for x 3x(x+1)(2x-7)(3x+4)^2(x-13)(x+7)=0

$3 x (x + 1) (2 x - 7) {(3 x + 4)}^{2} (x - 13) (x + 7) = 0$

Step 1

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

$x = 0$

$x + 1 = 0$

$2 x - 7 = 0$

${(3 x + 4)}^{2} = 0$

$x - 13 = 0$

$x + 7 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 4

Set $2 x - 7$ equal to $0$ and solve for $x$ .

Set $2 x - 7$ equal to $0$ .

$2 x - 7 = 0$

Solve $2 x - 7 = 0$ for $x$ .

Add $7$ to both sides of the equation.

$2 x = 7$

Divide each term in $2 x = 7$ by $2$ and simplify.

Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

Step 5

Set ${(3 x + 4)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(3 x + 4)}^{2}$ equal to $0$ .

${(3 x + 4)}^{2} = 0$

Solve ${(3 x + 4)}^{2} = 0$ for $x$ .

Set the $3 x + 4$ equal to $0$ .

$3 x + 4 = 0$

Solve for $x$ .

Subtract $4$ from 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 $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

Set $x - 13$ equal to $0$ and solve for $x$ .

Set $x - 13$ equal to $0$ .

$x - 13 = 0$

Add $13$ to both sides of the equation.

$x = 13$

Step 7

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 8

The final solution is all the values that make $3 x (x + 1) (2 x - 7) {(3 x + 4)}^{2} (x - 13) (x + 7) = 0$ true.

$x = 0, - 1, \frac{7}{2}, - \frac{4}{3}, 13, - 7$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = 0, - 1, \frac{7}{2}, - \frac{4}{3}, 13, - 7$

Decimal Form:

$x = 0, - 1, 3.5, - 1.\overline{3}, 13, - 7$

Mixed Number Form:

$x = 0, - 1, 3 \frac{1}{2}, - 1 \frac{1}{3}, 13, - 7$

Solve for x 3x(x+1)(2x-7)(3x+4)^2(x-13)(x+7)=0

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