Solve for x (0.3x^2-3x)(5x^3-0.2x^2)=0

$(0.3 x^{2} - 3 x) (5 x^{3} - 0.2 x^{2}) = 0$

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

$0.3 x^{2} - 3 x = 0$

$5 x^{3} - 0.2 x^{2} = 0$

Set $0.3 x^{2} - 3 x$ equal to $0$ and solve for $x$ .

Set $0.3 x^{2} - 3 x$ equal to $0$ .

$0.3 x^{2} - 3 x = 0$

Solve $0.3 x^{2} - 3 x = 0$ for $x$ .

Factor $0.3 x$ out of $0.3 x^{2} - 3 x$ .

Factor $0.3 x$ out of $0.3 x^{2}$ .

$0.3 x (x) - 3 x = 0$

Factor $0.3 x$ out of $- 3 x$ .

$0.3 x (x) + 0.3 x (- 10) = 0$

Factor $0.3 x$ out of $0.3 x (x) + 0.3 x (- 10)$ .

$0.3 x (x - 10) = 0$

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

$x = 0$

$x - 10 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x - 10 = 0$

Add $10$ to both sides of the equation.

$x = 10$

The final solution is all the values that make $0.3 x (x - 10) = 0$ true.

$x = 0, 10$

Set $5 x^{3} - 0.2 x^{2}$ equal to $0$ and solve for $x$ .

Set $5 x^{3} - 0.2 x^{2}$ equal to $0$ .

$5 x^{3} - 0.2 x^{2} = 0$

Solve $5 x^{3} - 0.2 x^{2} = 0$ for $x$ .

Factor $0.2 x^{2}$ out of $5 x^{3} - 0.2 x^{2}$ .

Factor $0.2 x^{2}$ out of $5 x^{3}$ .

$0.2 x^{2} (25 x) - 0.2 x^{2} = 0$

Factor $0.2 x^{2}$ out of $- 0.2 x^{2}$ .

$0.2 x^{2} (25 x) + 0.2 x^{2} (- 1) = 0$

Factor $0.2 x^{2}$ out of $0.2 x^{2} (25 x) + 0.2 x^{2} (- 1)$ .

$0.2 x^{2} (25 x - 1) = 0$

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

$x^{2} = 0$

$25 x - 1 = 0$

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 $25 x - 1$ equal to $0$ and solve for $x$ .

Set $25 x - 1$ equal to $0$ .

$25 x - 1 = 0$

Solve $25 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$25 x = 1$

Divide each term in $25 x = 1$ by $25$ and simplify.

Divide each term in $25 x = 1$ by $25$ .

$\frac{25 x}{25} = \frac{1}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x}{25} = \frac{1}{25}$

Divide $x$ by $1$ .

$x = \frac{1}{25}$

The final solution is all the values that make $0.2 x^{2} (25 x - 1) = 0$ true.

$x = 0, \frac{1}{25}$

The final solution is all the values that make $(0.3 x^{2} - 3 x) (5 x^{3} - 0.2 x^{2}) = 0$ true.

$x = 0, 10, \frac{1}{25}$

The result can be shown in multiple forms.

Exact Form:

$x = 0, 10, \frac{1}{25}$

Decimal Form:

$x = 0, 10, 0.04$

Solve for x (0.3x^2-3x)(5x^3-0.2x^2)=0

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