Trigonometry Examples

$(x^{2} + 3 x) \ln (10) = 0$

Step 1

Divide each term in $(x^{2} + 3 x) \ln (10) = 0$ by $\ln (10)$ and simplify.

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Step 1.1

Divide each term in $(x^{2} + 3 x) \ln (10) = 0$ by $\ln (10)$ .

$\frac{(x^{2} + 3 x) \ln (10)}{\ln (10)} = \frac{0}{\ln (10)}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $\ln (10)$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{(x^{2} + 3 x) \ln (10)}{\ln (10)} = \frac{0}{\ln (10)}$

Step 1.2.1.2

Divide $x^{2} + 3 x$ by $1$ .

$x^{2} + 3 x = \frac{0}{\ln (10)}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $\ln (10)$ .

$x^{2} + 3 x = 0$

Step 2

Factor $x$ out of $x^{2} + 3 x$ .

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Step 2.1

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

$x \cdot x + 3 x = 0$

Step 2.2

Factor $x$ out of $3 x$ .

$x \cdot x + x \cdot 3 = 0$

Step 2.3

Factor $x$ out of $x \cdot x + x \cdot 3$ .

$x (x + 3) = 0$

Step 3

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

$x = 0$

$x + 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 5.1

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

$x + 3 = 0$

Step 5.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 6

The final solution is all the values that make $x (x + 3) = 0$ true.

$x = 0, - 3$