Solve for r r^2-24=5r

$r^{2} - 24 = 5 r$

Step 1

Subtract $5 r$ from both sides of the equation.

$r^{2} - 24 - 5 r = 0$

Step 2

Factor $r^{2} - 24 - 5 r$ 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 $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Write the factored form using these integers.

$(r - 8) (r + 3) = 0$

Step 3

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

$r - 8 = 0$

$r + 3 = 0$

Step 4

Set $r - 8$ equal to $0$ and solve for $r$ .

Set $r - 8$ equal to $0$ .

$r - 8 = 0$

Add $8$ to both sides of the equation.

$r = 8$

Step 5

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

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

$r + 3 = 0$

Subtract $3$ from both sides of the equation.

$r = - 3$

Step 6

The final solution is all the values that make $(r - 8) (r + 3) = 0$ true.

$r = 8, - 3$

Solve for r r^2-24=5r

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