Solve 15p^2-27p-6=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

p_{1} = - \frac{1}{5}, p_{2} = 2

Alternative Form

p_{1} = - 0.2, p_{2} = 2

Evaluate

15 p^{2} - 27 p - 6 = 0

Factor the expression

More Steps

Evaluate

15 p^{2} - 27 p - 6

Rewrite the expression

3 \times 5 p^{2} - 3 \times 9 p - 3 \times 2

Factor out 3 from the expression

3 (5 p^{2} - 9 p - 2)

Factor the expression

More Steps

Evaluate

5 p^{2} - 9 p - 2

Rewrite the expression

5 p^{2} + (1 - 10) p - 2

Calculate

5 p^{2} + p - 10 p - 2

Rewrite the expression

p \times 5 p + p - 2 \times 5 p - 2

Factor out p from the expression

p (5 p + 1) - 2 \times 5 p - 2

Factor out - 2 from the expression

p (5 p + 1) - 2 (5 p + 1)

Factor out 5 p + 1 from the expression

(p - 2) (5 p + 1)

3 (p - 2) (5 p + 1)

3 (p - 2) (5 p + 1) = 0

Divide the terms

(p - 2) (5 p + 1) = 0

When the product of factors equals 0,at least one factor is 0

p - 2 = 0 5 p + 1 = 0

Solve the equation for p

More Steps

Evaluate

p - 2 = 0

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

p = 0 + 2

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

p = 2

p = 2 5 p + 1 = 0

Solve the equation for p

More Steps

Evaluate

5 p + 1 = 0

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

5 p = 0 - 1

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

5 p = - 1

Divide both sides

\frac{5 p}{5} = \frac{- 1}{5}

Divide the numbers

p = \frac{- 1}{5}

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

p = - \frac{1}{5}

p = 2 p = - \frac{1}{5}

Solution

p_{1} = - \frac{1}{5}, p_{2} = 2

Alternative Form

p_{1} = - 0.2, p_{2} = 2

Show Solution