Solve (-6 - 1/2p) (3/4p - 9)

Question

Simplify the expression

54 - \frac{3}{8} p^{2}

Evaluate

(- 6 - \frac{1}{2} p) (\frac{3}{4} p - 9)

Apply the distributive property

- 6 \times \frac{3}{4} p - (- 6 \times 9) - \frac{1}{2} p \times \frac{3}{4} p - (- \frac{1}{2} p \times 9)

Multiply the numbers

More Steps

Evaluate

- 6 \times \frac{3}{4}

Reduce the numbers

- 3 \times \frac{3}{2}

Multiply the numbers

- \frac{3 \times 3}{2}

Multiply the numbers

- \frac{9}{2}

- \frac{9}{2} p - (- 6 \times 9) - \frac{1}{2} p \times \frac{3}{4} p - (- \frac{1}{2} p \times 9)

Multiply the numbers

- \frac{9}{2} p - (- 54) - \frac{1}{2} p \times \frac{3}{4} p - (- \frac{1}{2} p \times 9)

Multiply the terms

More Steps

Evaluate

- \frac{1}{2} p \times \frac{3}{4} p

Multiply the numbers

More Steps

Evaluate

- \frac{1}{2} \times \frac{3}{4}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{3}{2 \times 4}

Multiply the numbers

- \frac{3}{8}

- \frac{3}{8} p \times p

Multiply the terms

- \frac{3}{8} p^{2}

- \frac{9}{2} p - (- 54) - \frac{3}{8} p^{2} - (- \frac{1}{2} p \times 9)

Multiply the numbers

- \frac{9}{2} p - (- 54) - \frac{3}{8} p^{2} - (- \frac{9}{2} p)

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

- \frac{9}{2} p + 54 - \frac{3}{8} p^{2} + \frac{9}{2} p

The sum of two opposites equals 0

More Steps

Evaluate

- \frac{9}{2} p + \frac{9}{2} p

Collect like terms

(- \frac{9}{2} + \frac{9}{2}) p

Add the coefficients

0 \times p

Calculate

0

0 + 54 - \frac{3}{8} p^{2}

Solution

54 - \frac{3}{8} p^{2}

Show Solution

Factor the expression

- \frac{3}{8} (12 + p) (p - 12)

Evaluate

(- 6 - \frac{1}{2} p) (\frac{3}{4} p - 9)

Factor the expression

- \frac{1}{2} (12 + p) (\frac{3}{4} p - 9)

Factor the expression

- \frac{1}{2} (12 + p) \times \frac{3}{4} (p - 12)

Solution

- \frac{3}{8} (12 + p) (p - 12)

Show Solution

Find the roots

p_{1} = - 12, p_{2} = 12

Evaluate

(- 6 - \frac{1}{2} p) (\frac{3}{4} p - 9)

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

(- 6 - \frac{1}{2} p) (\frac{3}{4} p - 9) = 0

Change the sign

(6 + \frac{1}{2} p) (\frac{3}{4} p - 9) = 0

Separate the equation into 2 possible cases

6 + \frac{1}{2} p = 0 \frac{3}{4} p - 9 = 0

Solve the equation

More Steps

Evaluate

6 + \frac{1}{2} p = 0

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

\frac{1}{2} p = 0 - 6

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

\frac{1}{2} p = - 6

Multiply by the reciprocal

\frac{1}{2} p \times 2 = - 6 \times 2

Multiply

p = - 6 \times 2

Multiply

p = - 12

p = - 12 \frac{3}{4} p - 9 = 0

Solve the equation

More Steps

Evaluate

\frac{3}{4} p - 9 = 0

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

\frac{3}{4} p = 0 + 9

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

\frac{3}{4} p = 9

Multiply by the reciprocal

\frac{3}{4} p \times \frac{4}{3} = 9 \times \frac{4}{3}

Multiply

p = 9 \times \frac{4}{3}

Multiply

More Steps

Evaluate

9 \times \frac{4}{3}

Reduce the numbers

3 \times 4

Multiply the numbers

12

p = 12

p = - 12 p = 12

Solution

p_{1} = - 12, p_{2} = 12

Show Solution