Basic Math Examples

$5 s^{2} - 11 s = 12$

Step 1

Subtract $12$ from both sides of the equation.

$5 s^{2} - 11 s - 12 = 0$

Step 2

Factor by grouping.

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Step 2.1

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 $a \cdot c = 5 \cdot - 12 = - 60$ and whose sum is $b = - 11$ .

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Step 2.1.1

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

$5 s^{2} - 11 s - 12 = 0$

Step 2.1.2

Rewrite $- 11$ as $4$ plus $- 15$

$5 s^{2} + (4 - 15) s - 12 = 0$

Step 2.1.3

Apply the distributive property.

$5 s^{2} + 4 s - 15 s - 12 = 0$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$(5 s^{2} + 4 s) - 15 s - 12 = 0$

Step 2.2.2

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

$s (5 s + 4) - 3 (5 s + 4) = 0$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $5 s + 4$ .

$(5 s + 4) (s - 3) = 0$

Step 3

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

$5 s + 4 = 0$

$s - 3 = 0$

Step 4

Set $5 s + 4$ equal to $0$ and solve for $s$ .

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Step 4.1

Set $5 s + 4$ equal to $0$ .

$5 s + 4 = 0$

Step 4.2

Solve $5 s + 4 = 0$ for $s$ .

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$5 s = - 4$

Step 4.2.2

Divide each term in $5 s = - 4$ by $5$ and simplify.

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Step 4.2.2.1

Divide each term in $5 s = - 4$ by $5$ .

$\frac{5 s}{5} = \frac{- 4}{5}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $5$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{5 s}{5} = \frac{- 4}{5}$

Step 4.2.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{- 4}{5}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Move the negative in front of the fraction.

$s = - \frac{4}{5}$

Step 5

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

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Step 5.1

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

$s - 3 = 0$

Step 5.2

Add $3$ to both sides of the equation.

$s = 3$

Step 6

The final solution is all the values that make $(5 s + 4) (s - 3) = 0$ true.

$s = - \frac{4}{5}, 3$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{4}{5}, 3$

Decimal Form:

$s = - 0.8, 3$