Solve for x -2x(10x-3)(x^2+100)=0

$- 2 x (10 x - 3) (x^{2} + 100) = 0$

Step 1

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

$x = 0$

$10 x - 3 = 0$

$x^{2} + 100 = 0$

Step 2

Set $x$ equal to $0$ .

$x = 0$

Step 3

Set $10 x - 3$ equal to $0$ and solve for $x$ .

Set $10 x - 3$ equal to $0$ .

$10 x - 3 = 0$

Solve $10 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$10 x = 3$

Divide each term in $10 x = 3$ by $10$ and simplify.

Divide each term in $10 x = 3$ by $10$ .

$\frac{10 x}{10} = \frac{3}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{3}{10}$

Divide $x$ by $1$ .

$x = \frac{3}{10}$

Step 4

Set $x^{2} + 100$ equal to $0$ and solve for $x$ .

Set $x^{2} + 100$ equal to $0$ .

$x^{2} + 100 = 0$

Solve $x^{2} + 100 = 0$ for $x$ .

Subtract $100$ from both sides of the equation.

$x^{2} = - 100$

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

$x = \pm \sqrt{- 100}$

Simplify $\pm \sqrt{- 100}$ .

Rewrite $- 100$ as $- 1 (100)$ .

$x = \pm \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{100}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$x = \pm i \cdot \sqrt{10^{2}}$

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

$x = \pm i \cdot 10$

Move $10$ to the left of $i$ .

$x = \pm 10 i$

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.

$x = 10 i$

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

$x = - 10 i$

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

$x = 10 i, - 10 i$

Step 5

The final solution is all the values that make $- 2 x (10 x - 3) (x^{2} + 100) = 0$ true.

$x = 0, \frac{3}{10}, 10 i, - 10 i$

Solve for x -2x(10x-3)(x^2+100)=0

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