Finite Math Examples

$3 y^{2} - 6 y = - 3$

Step 1

Add $3$ to both sides of the equation.

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

Step 2

Factor $3$ out of $3 y^{2} - 6 y + 3$ .

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Step 2.1

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

$3 (y^{2}) - 6 y + 3 = 0$

Step 2.2

Factor $3$ out of $- 6 y$ .

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

Step 2.3

Factor $3$ out of $3$ .

$3 (y^{2}) + 3 (- 2 y) + 3 (1) = 0$

Step 2.4

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

$3 (y^{2} - 2 y) + 3 (1) = 0$

Step 2.5

Factor $3$ out of $3 (y^{2} - 2 y) + 3 (1)$ .

$3 (y^{2} - 2 y + 1) = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $1$ as $1^{2}$ .

$3 (y^{2} - 2 y + 1^{2}) = 0$

Step 3.2

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

$2 y = 2 \cdot y \cdot 1$

Step 3.3

Rewrite the polynomial.

$3 (y^{2} - 2 \cdot y \cdot 1 + 1^{2}) = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = y$ and $b = 1$ .

$3 {(y - 1)}^{2} = 0$

Step 4

Divide each term in $3 {(y - 1)}^{2} = 0$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 {(y - 1)}^{2} = 0$ by $3$ .

$\frac{3 {(y - 1)}^{2}}{3} = \frac{0}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 {(y - 1)}^{2}}{3} = \frac{0}{3}$

Step 4.2.1.2

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

${(y - 1)}^{2} = \frac{0}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $3$ .

${(y - 1)}^{2} = 0$

Step 5

Set the $y - 1$ equal to $0$ .

$y - 1 = 0$

Step 6

Add $1$ to both sides of the equation.

$y = 1$