Find the Roots (Zeros) x^2(6x-11)(7x-8)=0

$x^{2} (6 x - 11) (7 x - 8) = 0$

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

$x^{2} = 0$

$6 x - 11 = 0$

$7 x - 8 = 0$

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set $6 x - 11$ equal to $0$ and solve for $x$ .

Set $6 x - 11$ equal to $0$ .

$6 x - 11 = 0$

Solve $6 x - 11 = 0$ for $x$ .

Add $11$ to both sides of the equation.

$6 x = 11$

Divide each term in $6 x = 11$ by $6$ and simplify.

Divide each term in $6 x = 11$ by $6$ .

$\frac{6 x}{6} = \frac{11}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{11}{6}$

Divide $x$ by $1$ .

$x = \frac{11}{6}$

Set $7 x - 8$ equal to $0$ and solve for $x$ .

Set $7 x - 8$ equal to $0$ .

$7 x - 8 = 0$

Solve $7 x - 8 = 0$ for $x$ .

Add $8$ to both sides of the equation.

$7 x = 8$

Divide each term in $7 x = 8$ by $7$ and simplify.

Divide each term in $7 x = 8$ by $7$ .

$\frac{7 x}{7} = \frac{8}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{8}{7}$

Divide $x$ by $1$ .

$x = \frac{8}{7}$

The final solution is all the values that make $x^{2} (6 x - 11) (7 x - 8) = 0$ true.

$x = 0, \frac{11}{6}, \frac{8}{7}$

Find the Roots (Zeros) x^2(6x-11)(7x-8)=0

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