Trigonometry Examples

$(2 x - 1) (3 x + 2) = 0$

Step 1

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

$2 x - 1 = 0$

$3 x + 2 = 0$

Step 2

Set $2 x - 1$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Step 2.2

Solve $2 x - 1 = 0$ for $x$ .

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Step 2.2.1

Add $1$ to both sides of the equation.

$2 x = 1$

Step 2.2.2

Divide each term in $2 x = 1$ by $2$ and simplify.

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Step 2.2.2.1

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Step 2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Step 3

Set $3 x + 2$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $3 x + 2$ equal to $0$ .

$3 x + 2 = 0$

Step 3.2

Solve $3 x + 2 = 0$ for $x$ .

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Step 3.2.1

Subtract $2$ from both sides of the equation.

$3 x = - 2$

Step 3.2.2

Divide each term in $3 x = - 2$ by $3$ and simplify.

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Step 3.2.2.1

Divide each term in $3 x = - 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2}{3}$

Step 3.2.2.2

Simplify the left side.

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Step 3.2.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2}{3}$

Step 3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{3}$

Step 3.2.2.3

Simplify the right side.

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Step 3.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

Step 4

The final solution is all the values that make $(2 x - 1) (3 x + 2) = 0$ true.

$x = \frac{1}{2}, - \frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - \frac{2}{3}$

Decimal Form:

$x = 0.5, - 0.\overline{6}$