Solve by Factoring 6y^2+36=30y

$6 y^{2} + 36 = 30 y$

Step 1

Subtract $30 y$ from both sides of the equation.

$6 y^{2} + 36 - 30 y = 0$

Step 2

Factor $6$ out of $6 y^{2} + 36 - 30 y$ .

Factor $6$ out of $6 y^{2}$ .

$6 (y^{2}) + 36 - 30 y = 0$

Factor $6$ out of $36$ .

$6 y^{2} + 6 \cdot 6 - 30 y = 0$

Factor $6$ out of $- 30 y$ .

$6 y^{2} + 6 \cdot 6 + 6 (- 5 y) = 0$

Factor $6$ out of $6 y^{2} + 6 \cdot 6$ .

$6 (y^{2} + 6) + 6 (- 5 y) = 0$

Factor $6$ out of $6 (y^{2} + 6) + 6 (- 5 y)$ .

$6 (y^{2} + 6 - 5 y) = 0$

Step 3

Factor.

Factor $y^{2} + 6 - 5 y$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $- 5$ .

$- 3, - 2$

Write the factored form using these integers.

$6 ((y - 3) (y - 2)) = 0$

Remove unnecessary parentheses.

$6 (y - 3) (y - 2) = 0$

Step 4

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

$y - 3 = 0$

$y - 2 = 0$

Step 5

Set $y - 3$ equal to $0$ and solve for $y$ .

Set $y - 3$ equal to $0$ .

$y - 3 = 0$

Add $3$ to both sides of the equation.

$y = 3$

Step 6

Set $y - 2$ equal to $0$ and solve for $y$ .

Set $y - 2$ equal to $0$ .

$y - 2 = 0$

Add $2$ to both sides of the equation.

$y = 2$

Step 7

The final solution is all the values that make $6 (y - 3) (y - 2) = 0$ true.

$y = 3, 2$

Solve by Factoring 6y^2+36=30y

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