Solve ( - 6s-2) ( - 3s-6)

Question

Simplify the expression

18 s^{2} + 42 s + 12

Evaluate

(- 6 s - 2) (- 3 s - 6)

Apply the distributive property

- 6 s (- 3 s) - (- 6 s \times 6) - 2 (- 3 s) - (- 2 \times 6)

Multiply the terms

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Evaluate

- 6 s (- 3 s)

Multiply the numbers

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Evaluate

- 6 (- 3)

Multiplying or dividing an even number of negative terms equals a positive

6 \times 3

Multiply the numbers

18

18 s \times s

Multiply the terms

18 s^{2}

18 s^{2} - (- 6 s \times 6) - 2 (- 3 s) - (- 2 \times 6)

Multiply the numbers

18 s^{2} - (- 36 s) - 2 (- 3 s) - (- 2 \times 6)

Multiply the numbers

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Evaluate

- 2 (- 3)

Multiplying or dividing an even number of negative terms equals a positive

2 \times 3

Multiply the numbers

6

18 s^{2} - (- 36 s) + 6 s - (- 2 \times 6)

Multiply the numbers

18 s^{2} - (- 36 s) + 6 s - (- 12)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

18 s^{2} + 36 s + 6 s + 12

Solution

More Steps

Evaluate

36 s + 6 s

Collect like terms by calculating the sum or difference of their coefficients

(36 + 6) s

Add the numbers

42 s

18 s^{2} + 42 s + 12

Show Solution

Factor the expression

6 (3 s + 1) (s + 2)

Evaluate

(- 6 s - 2) (- 3 s - 6)

Factor the expression

- 2 (3 s + 1) (- 3 s - 6)

Factor the expression

- 2 (3 s + 1) (- 3) (s + 2)

Solution

6 (3 s + 1) (s + 2)

Show Solution

Find the roots

s_{1} = - 2, s_{2} = - \frac{1}{3}

Alternative Form

s_{1} = - 2, s_{2} = - 0. \dot{3}

Evaluate

(- 6 s - 2) (- 3 s - 6)

To find the roots of the expression,set the expression equal to 0

(- 6 s - 2) (- 3 s - 6) = 0

Change the sign

(6 s + 2) (- 3 s - 6) = 0

Separate the equation into 2 possible cases

6 s + 2 = 0 - 3 s - 6 = 0

Solve the equation

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Evaluate

6 s + 2 = 0

Move the constant to the right-hand side and change its sign

6 s = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

6 s = - 2

Divide both sides

\frac{6 s}{6} = \frac{- 2}{6}

Divide the numbers

s = \frac{- 2}{6}

Divide the numbers

More Steps

Evaluate

\frac{- 2}{6}

Cancel out the common factor 2

\frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{3}

s = - \frac{1}{3}

s = - \frac{1}{3} - 3 s - 6 = 0

Solve the equation

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Evaluate

- 3 s - 6 = 0

Move the constant to the right-hand side and change its sign

- 3 s = 0 + 6

Removing 0 doesn't change the value,so remove it from the expression

- 3 s = 6

Change the signs on both sides of the equation

3 s = - 6

Divide both sides

\frac{3 s}{3} = \frac{- 6}{3}

Divide the numbers

s = \frac{- 6}{3}

Divide the numbers

More Steps

Evaluate

\frac{- 6}{3}

Reduce the numbers

\frac{- 2}{1}

Calculate

- 2

s = - 2

s = - \frac{1}{3} s = - 2

Solution

s_{1} = - 2, s_{2} = - \frac{1}{3}

Alternative Form

s_{1} = - 2, s_{2} = - 0. \dot{3}

Show Solution