Solve for x 3(x-4)(49x^2-16)=0

$3 (x - 4) (49 x^{2} - 16) = 0$

Step 1

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

$x - 4 = 0$

$49 x^{2} - 16 = 0$

Step 2

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.

$x = 4$

Step 3

Set $49 x^{2} - 16$ equal to $0$ and solve for $x$ .

Set $49 x^{2} - 16$ equal to $0$ .

$49 x^{2} - 16 = 0$

Solve $49 x^{2} - 16 = 0$ for $x$ .

Add $16$ to both sides of the equation.

$49 x^{2} = 16$

Divide each term in $49 x^{2} = 16$ by $49$ and simplify.

Divide each term in $49 x^{2} = 16$ by $49$ .

$\frac{49 x^{2}}{49} = \frac{16}{49}$

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

$\frac{49 x^{2}}{49} = \frac{16}{49}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{16}{49}$

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

$x = \pm \sqrt{\frac{16}{49}}$

Simplify $\pm \sqrt{\frac{16}{49}}$ .

Rewrite $\sqrt{\frac{16}{49}}$ as $\frac{\sqrt{16}}{\sqrt{49}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{49}}$

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{49}}$

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

$x = \pm \frac{4}{\sqrt{49}}$

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{4}{\sqrt{7^{2}}}$

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

$x = \pm \frac{4}{7}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{4}{7}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{4}{7}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{4}{7}, - \frac{4}{7}$

Step 4

The final solution is all the values that make $3 (x - 4) (49 x^{2} - 16) = 0$ true.

$x = 4, \frac{4}{7}, - \frac{4}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4, \frac{4}{7}, - \frac{4}{7}$

Decimal Form:

$x = 4, 0.\overline{571428}, - 0.\overline{571428}$

Solve for x 3(x-4)(49x^2-16)=0

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