Finite Math Examples

$3 x (x + 2) = 6 x$

Step 1

Simplify $3 x (x + 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 x (x + 2) = 6 x$

Step 1.2

Simplify by adding zeros.

$3 x (x + 2) = 6 x$

Step 1.3

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 2 = 6 x$

Step 1.4

Multiply $x$ by $x$ by adding the exponents.

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Step 1.4.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot 2 = 6 x$

Step 1.4.2

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot 2 = 6 x$

Step 1.5

Multiply $2$ by $3$ .

$3 x^{2} + 6 x = 6 x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $6 x$ from both sides of the equation.

$3 x^{2} + 6 x - 6 x = 0$

Step 2.2

Combine the opposite terms in $3 x^{2} + 6 x - 6 x$ .

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Step 2.2.1

Subtract $6 x$ from $6 x$ .

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

Step 2.2.2

Add $3 x^{2}$ and $0$ .

$3 x^{2} = 0$

Step 3

Divide each term in $3 x^{2} = 0$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x^{2} = 0$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{0}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{0}{3}$

Step 3.2.1.2

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

$x^{2} = \frac{0}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $3$ .

$x^{2} = 0$

Step 4

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

$x = \pm \sqrt{0}$

Step 5

Simplify $\pm \sqrt{0}$ .

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Step 5.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 5.2

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

$x = \pm 0$

Step 5.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 6