Finite Math Examples

$3 w^{2} - 12 w + 12 = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $3$ out of $3 w^{2} - 12 w + 12$ .

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Step 1.1.1

Factor $3$ out of $3 w^{2}$ .

$3 (w^{2}) - 12 w + 12 = 0$

Step 1.1.2

Factor $3$ out of $- 12 w$ .

$3 (w^{2}) + 3 (- 4 w) + 12 = 0$

Step 1.1.3

Factor $3$ out of $12$ .

$3 w^{2} + 3 (- 4 w) + 3 \cdot 4 = 0$

Step 1.1.4

Factor $3$ out of $3 w^{2} + 3 (- 4 w)$ .

$3 (w^{2} - 4 w) + 3 \cdot 4 = 0$

Step 1.1.5

Factor $3$ out of $3 (w^{2} - 4 w) + 3 \cdot 4$ .

$3 (w^{2} - 4 w + 4) = 0$

Step 1.2

Factor using the perfect square rule.

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Step 1.2.1

Rewrite $4$ as $2^{2}$ .

$3 (w^{2} - 4 w + 2^{2}) = 0$

Step 1.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 w = 2 \cdot w \cdot 2$

Step 1.2.3

Rewrite the polynomial.

$3 (w^{2} - 2 \cdot w \cdot 2 + 2^{2}) = 0$

Step 1.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = w$ and $b = 2$ .

$3 {(w - 2)}^{2} = 0$

Step 2

Divide each term in $3 {(w - 2)}^{2} = 0$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 {(w - 2)}^{2} = 0$ by $3$ .

$\frac{3 {(w - 2)}^{2}}{3} = \frac{0}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 {(w - 2)}^{2}}{3} = \frac{0}{3}$

Step 2.2.1.2

Divide ${(w - 2)}^{2}$ by $1$ .

${(w - 2)}^{2} = \frac{0}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $3$ .

${(w - 2)}^{2} = 0$

Step 3

Set the $w - 2$ equal to $0$ .

$w - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$w = 2$