Find the Roots (Zeros) f(x)=3/2(x-2)

$f (x) = \frac{3}{2} (x - 2)$

Step 1

Set $\frac{3}{2} \cdot (x - 2)$ equal to $0$ .

$\frac{3}{2} \cdot (x - 2) = 0$

Step 2

Solve for $x$ .

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} (\frac{3}{2} \cdot (x - 2)) = \frac{2}{3} \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} (\frac{3}{2} \cdot (x - 2))$ .

Apply the distributive property.

$\frac{2}{3} (\frac{3}{2} x + \frac{3}{2} \cdot - 2) = \frac{2}{3} \cdot 0$

Combine $\frac{3}{2}$ and $x$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{3}{2} \cdot - 2) = \frac{2}{3} \cdot 0$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{3}{2} \cdot (2 (- 1))) = \frac{2}{3} \cdot 0$

Cancel the common factor.

$\frac{2}{3} (\frac{3 x}{2} + \frac{3}{2} \cdot (2 \cdot - 1)) = \frac{2}{3} \cdot 0$

Rewrite the expression.

$\frac{2}{3} (\frac{3 x}{2} + 3 \cdot - 1) = \frac{2}{3} \cdot 0$

Multiply $3$ by $- 1$ .

$\frac{2}{3} (\frac{3 x}{2} - 3) = \frac{2}{3} \cdot 0$

Apply the distributive property.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot - 3 = \frac{2}{3} \cdot 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot - 3 = \frac{2}{3} \cdot 0$

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot - 3 = \frac{2}{3} \cdot 0$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{2}{3} \cdot - 3 = \frac{2}{3} \cdot 0$

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot - 3 = \frac{2}{3} \cdot 0$

Rewrite the expression.

$x + \frac{2}{3} \cdot - 3 = \frac{2}{3} \cdot 0$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$x + \frac{2}{3} \cdot (3 (- 1)) = \frac{2}{3} \cdot 0$

Cancel the common factor.

$x + \frac{2}{3} \cdot (3 \cdot - 1) = \frac{2}{3} \cdot 0$

Rewrite the expression.

$x + 2 \cdot - 1 = \frac{2}{3} \cdot 0$

Multiply $2$ by $- 1$ .

$x - 2 = \frac{2}{3} \cdot 0$

Simplify the right side.

Multiply $\frac{2}{3}$ by $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 3

Find the Roots (Zeros) f(x)=3/2(x-2)

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