Solve by Factoring 2b^3-30b=4b^2

$2 b^{3} - 30 b = 4 b^{2}$

Step 1

Subtract $4 b^{2}$ from both sides of the equation.

$2 b^{3} - 30 b - 4 b^{2} = 0$

Step 2

Factor $2 b$ out of $2 b^{3} - 30 b - 4 b^{2}$ .

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

$2 b (b^{2}) - 30 b - 4 b^{2} = 0$

Factor $2 b$ out of $- 30 b$ .

$2 b (b^{2}) + 2 b (- 15) - 4 b^{2} = 0$

Factor $2 b$ out of $- 4 b^{2}$ .

$2 b (b^{2}) + 2 b (- 15) + 2 b (- 2 b) = 0$

Factor $2 b$ out of $2 b (b^{2}) + 2 b (- 15)$ .

$2 b (b^{2} - 15) + 2 b (- 2 b) = 0$

Factor $2 b$ out of $2 b (b^{2} - 15) + 2 b (- 2 b)$ .

$2 b (b^{2} - 15 - 2 b) = 0$

Step 3

Factor.

Factor $b^{2} - 15 - 2 b$ 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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Write the factored form using these integers.

$2 b ((b - 5) (b + 3)) = 0$

Remove unnecessary parentheses.

$2 b (b - 5) (b + 3) = 0$

Step 4

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

$b = 0$

$b - 5 = 0$

$b + 3 = 0$

Step 5

Set $b$ equal to $0$ .

$b = 0$

Step 6

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

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

$b - 5 = 0$

Add $5$ to both sides of the equation.

$b = 5$

Step 7

Set $b + 3$ equal to $0$ and solve for $b$ .

Set $b + 3$ equal to $0$ .

$b + 3 = 0$

Subtract $3$ from both sides of the equation.

$b = - 3$

Step 8

The final solution is all the values that make $2 b (b - 5) (b + 3) = 0$ true.

$b = 0, 5, - 3$

Solve by Factoring 2b^3-30b=4b^2

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