Solve -4(-3p^6)-5p=10p

Question

Solve the equation

p_{1} = 0, p_{2} = \frac{5 40}{2}

Alternative Form

p_{1} = 0, p_{2} \approx 1.04564

Evaluate

- 4 (- 3 p^{6}) - 5 p = 10 p

Multiply the numbers

More Steps

Evaluate

- 4 (- 3)

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

4 \times 3

Multiply the numbers

12

12 p^{6} - 5 p = 10 p

Move the expression to the left side

12 p^{6} - 5 p - 10 p = 0

Subtract the terms

More Steps

Evaluate

- 5 p - 10 p

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

(- 5 - 10) p

Subtract the numbers

- 15 p

12 p^{6} - 15 p = 0

Factor the expression

3 p (4 p^{5} - 5) = 0

Divide both sides

p (4 p^{5} - 5) = 0

Separate the equation into 2 possible cases

p = 0 4 p^{5} - 5 = 0

Solve the equation

More Steps

Evaluate

4 p^{5} - 5 = 0

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

4 p^{5} = 0 + 5

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

4 p^{5} = 5

Divide both sides

\frac{4 p ^{5}}{4} = \frac{5}{4}

Divide the numbers

p^{5} = \frac{5}{4}

Take the 5 -th root on both sides of the equation

5 p^{5} = 5 \frac{5}{4}

Calculate

p = 5 \frac{5}{4}

Simplify the root

More Steps

Evaluate

5 \frac{5}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5 5}{5 4}

Multiply by the Conjugate

\frac{5 5 \times 5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{5 5 \times 2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

\frac{2 5 40}{5 4 \times 5 4 ^{4}}

Multiply the numbers

\frac{2 5 40}{2 ^{2}}

Reduce the fraction

\frac{5 40}{2}

p = \frac{5 40}{2}

p = 0 p = \frac{5 40}{2}

Solution

p_{1} = 0, p_{2} = \frac{5 40}{2}

Alternative Form

p_{1} = 0, p_{2} \approx 1.04564

Show Solution