Solve for s s(11-s)=24

$s (11 - s) = 24$

Simplify $s (11 - s)$ .

Simplify by multiplying through.

Apply the distributive property.

$s \cdot 11 + s (- s) = 24$

Reorder.

Move $11$ to the left of $s$ .

$11 \cdot s + s (- s) = 24$

Rewrite using the commutative property of multiplication.

$11 \cdot s - s \cdot s = 24$

Multiply $s$ by $s$ by adding the exponents.

Move $s$ .

$11 s - (s \cdot s) = 24$

Multiply $s$ by $s$ .

$11 s - s^{2} = 24$

Subtract $24$ from both sides of the equation.

$11 s - s^{2} - 24 = 0$

Factor the left side of the equation.

Factor $- 1$ out of $11 s - s^{2} - 24$ .

Reorder $11 s$ and $- s^{2}$ .

$- s^{2} + 11 s - 24 = 0$

Factor $- 1$ out of $- s^{2}$ .

$- (s^{2}) + 11 s - 24 = 0$

Factor $- 1$ out of $11 s$ .

$- (s^{2}) - (- 11 s) - 24 = 0$

Rewrite $- 24$ as $- 1 (24)$ .

$- (s^{2}) - (- 11 s) - 1 \cdot 24 = 0$

Factor $- 1$ out of $- (s^{2}) - (- 11 s)$ .

$- (s^{2} - 11 s) - 1 \cdot 24 = 0$

Factor $- 1$ out of $- (s^{2} - 11 s) - 1 (24)$ .

$- (s^{2} - 11 s + 24) = 0$

Factor.

Factor $s^{2} - 11 s + 24$ 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 $- 11$ .

$- 8, - 3$

Write the factored form using these integers.

$- ((s - 8) (s - 3)) = 0$

Remove unnecessary parentheses.

$- (s - 8) (s - 3) = 0$

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

$s - 8 = 0$

$s - 3 = 0$

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

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

$s - 8 = 0$

Add $8$ to both sides of the equation.

$s = 8$

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

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

$s - 3 = 0$

Add $3$ to both sides of the equation.

$s = 3$

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

$s = 8, 3$

Solve for s s(11-s)=24

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