Solve 16x^4-96x^3 216x^2-216x 81(2x-3)

Question

Simplify the expression

16 x^{4} - 20736 x^{5} - 34992 x^{2} + 52488 x

Evaluate

16 x^{4} - 96 x^{3} \times 216 x^{2} - 216 x \times 81 (2 x - 3)

Multiply

More Steps

Multiply the terms

- 96 x^{3} \times 216 x^{2}

Multiply the terms

- 20736 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 20736 x^{3 + 2}

Add the numbers

- 20736 x^{5}

16 x^{4} - 20736 x^{5} - 216 x \times 81 (2 x - 3)

Multiply the terms

16 x^{4} - 20736 x^{5} - 17496 x (2 x - 3)

Solution

More Steps

Evaluate

- 17496 x (2 x - 3)

Apply the distributive property

- 17496 x \times 2 x - (- 17496 x \times 3)

Multiply the terms

More Steps

Evaluate

- 17496 x \times 2 x

Multiply the numbers

- 34992 x \times x

Multiply the terms

- 34992 x^{2}

- 34992 x^{2} - (- 17496 x \times 3)

Multiply the numbers

- 34992 x^{2} - (- 52488 x)

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

- 34992 x^{2} + 52488 x

16 x^{4} - 20736 x^{5} - 34992 x^{2} + 52488 x

Show Solution

Factor the expression

8 x (2 x^{3} - 2592 x^{4} - 4374 x + 6561)

Evaluate

16 x^{4} - 96 x^{3} \times 216 x^{2} - 216 x \times 81 (2 x - 3)

Multiply

More Steps

Multiply the terms

96 x^{3} \times 216 x^{2}

Multiply the terms

20736 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

20736 x^{3 + 2}

Add the numbers

20736 x^{5}

16 x^{4} - 20736 x^{5} - 216 x \times 81 (2 x - 3)

Multiply the terms

16 x^{4} - 20736 x^{5} - 17496 x (2 x - 3)

Rewrite the expression

8 x (2 x^{3} - 2592 x^{4}) - 8 x \times 2187 (2 x - 3)

Factor out 8 x from the expression

8 x (2 x^{3} - 2592 x^{4} - 2187 (2 x - 3))

Solution

8 x (2 x^{3} - 2592 x^{4} - 4374 x + 6561)

Show Solution

Find the roots

x_{1} \approx - 1.49978, x_{2} = 0, x_{3} \approx 0.97183

Evaluate

16 x^{4} - 96 x^{3} \times 216 x^{2} - 216 x \times 81 (2 x - 3)

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

16 x^{4} - 96 x^{3} \times 216 x^{2} - 216 x \times 81 (2 x - 3) = 0

Multiply

More Steps

Multiply the terms

96 x^{3} \times 216 x^{2}

Multiply the terms

20736 x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

20736 x^{3 + 2}

Add the numbers

20736 x^{5}

16 x^{4} - 20736 x^{5} - 216 x \times 81 (2 x - 3) = 0

Multiply the terms

16 x^{4} - 20736 x^{5} - 17496 x (2 x - 3) = 0

Calculate

More Steps

Evaluate

- 17496 x (2 x - 3)

Apply the distributive property

- 17496 x \times 2 x - (- 17496 x \times 3)

Multiply the terms

More Steps

Evaluate

- 17496 x \times 2 x

Multiply the numbers

- 34992 x \times x

Multiply the terms

- 34992 x^{2}

- 34992 x^{2} - (- 17496 x \times 3)

Multiply the numbers

- 34992 x^{2} - (- 52488 x)

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

- 34992 x^{2} + 52488 x

16 x^{4} - 20736 x^{5} - 34992 x^{2} + 52488 x = 0

Factor the expression

8 x (2 x^{3} - 2592 x^{4} - 4374 x + 6561) = 0

Divide both sides

x (2 x^{3} - 2592 x^{4} - 4374 x + 6561) = 0

Separate the equation into 2 possible cases

x = 0 2 x^{3} - 2592 x^{4} - 4374 x + 6561 = 0

Solve the equation

x = 0 x \approx - 1.49978 x \approx 0.97183

Solution

x_{1} \approx - 1.49978, x_{2} = 0, x_{3} \approx 0.97183

Show Solution