Basic Math Examples

$5 y^{2} = - 15 y + 200$

Step 1

Add $15 y$ to both sides of the equation.

$5 y^{2} + 15 y = 200$

Step 2

Subtract $200$ from both sides of the equation.

$5 y^{2} + 15 y - 200 = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $5$ out of $5 y^{2} + 15 y - 200$ .

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Step 3.1.1

Factor $5$ out of $5 y^{2}$ .

$5 (y^{2}) + 15 y - 200 = 0$

Step 3.1.2

Factor $5$ out of $15 y$ .

$5 (y^{2}) + 5 (3 y) - 200 = 0$

Step 3.1.3

Factor $5$ out of $- 200$ .

$5 y^{2} + 5 (3 y) + 5 \cdot - 40 = 0$

Step 3.1.4

Factor $5$ out of $5 y^{2} + 5 (3 y)$ .

$5 (y^{2} + 3 y) + 5 \cdot - 40 = 0$

Step 3.1.5

Factor $5$ out of $5 (y^{2} + 3 y) + 5 \cdot - 40$ .

$5 (y^{2} + 3 y - 40) = 0$

Step 3.2

Factor.

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Step 3.2.1

Factor $y^{2} + 3 y - 40$ using the AC method.

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Step 3.2.1.1

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 $- 40$ and whose sum is $3$ .

$- 5, 8$

Step 3.2.1.2

Write the factored form using these integers.

$5 ((y - 5) (y + 8)) = 0$

Step 3.2.2

Remove unnecessary parentheses.

$5 (y - 5) (y + 8) = 0$

Step 4

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

$y - 5 = 0$

$y + 8 = 0$

Step 5

Set $y - 5$ equal to $0$ and solve for $y$ .

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Step 5.1

Set $y - 5$ equal to $0$ .

$y - 5 = 0$

Step 5.2

Add $5$ to both sides of the equation.

$y = 5$

Step 6

Set $y + 8$ equal to $0$ and solve for $y$ .

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Step 6.1

Set $y + 8$ equal to $0$ .

$y + 8 = 0$

Step 6.2

Subtract $8$ from both sides of the equation.

$y = - 8$

Step 7

The final solution is all the values that make $5 (y - 5) (y + 8) = 0$ true.

$y = 5, - 8$