Solve for s 3s^2-22s=16

$3 s^{2} - 22 s = 16$

Step 1

Subtract $16$ from both sides of the equation.

$3 s^{2} - 22 s - 16 = 0$

Step 2

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 16 = - 48$ and whose sum is $b = - 22$ .

Factor $- 22$ out of $- 22 s$ .

$3 s^{2} - 22 s - 16 = 0$

Rewrite $- 22$ as $2$ plus $- 24$

$3 s^{2} + (2 - 24) s - 16 = 0$

Apply the distributive property.

$3 s^{2} + 2 s - 24 s - 16 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 s^{2} + 2 s) - 24 s - 16 = 0$

Factor out the greatest common factor (GCF) from each group.

$s (3 s + 2) - 8 (3 s + 2) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 s + 2$ .

$(3 s + 2) (s - 8) = 0$

Step 3

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

$3 s + 2 = 0$

$s - 8 = 0$

Step 4

Set $3 s + 2$ equal to $0$ and solve for $s$ .

Set $3 s + 2$ equal to $0$ .

$3 s + 2 = 0$

Solve $3 s + 2 = 0$ for $s$ .

Subtract $2$ from both sides of the equation.

$3 s = - 2$

Divide each term in $3 s = - 2$ by $3$ and simplify.

Divide each term in $3 s = - 2$ by $3$ .

$\frac{3 s}{3} = \frac{- 2}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 s}{3} = \frac{- 2}{3}$

Divide $s$ by $1$ .

$s = \frac{- 2}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$s = - \frac{2}{3}$

Step 5

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.

$s = 8$

Step 6

The final solution is all the values that make $(3 s + 2) (s - 8) = 0$ true.

$s = - \frac{2}{3}, 8$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{2}{3}, 8$

Decimal Form:

$s = - 0.\overline{6}, 8$

Solve for s 3s^2-22s=16

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