Solve x^26x-27x^2-6x 9-6x-3

Question

Simplify the expression

6 x^{3} - 27 x^{2} - 60 x - 3

Evaluate

x^{2} \times 6 x - 27 x^{2} - 6 x \times 9 - 6 x - 3

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

6 x^{3} - 27 x^{2} - 6 x \times 9 - 6 x - 3

Multiply the terms

6 x^{3} - 27 x^{2} - 54 x - 6 x - 3

Solution

More Steps

Evaluate

- 54 x - 6 x

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

(- 54 - 6) x

Subtract the numbers

- 60 x

6 x^{3} - 27 x^{2} - 60 x - 3

Show Solution

Factor the expression

3 (2 x^{3} - 9 x^{2} - 20 x - 1)

Evaluate

x^{2} \times 6 x - 27 x^{2} - 6 x \times 9 - 6 x - 3

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

6 x^{3} - 27 x^{2} - 6 x \times 9 - 6 x - 3

Multiply the terms

6 x^{3} - 27 x^{2} - 54 x - 6 x - 3

Subtract the terms

More Steps

Simplify

6 x^{3} - 27 x^{2} - 54 x - 6 x

Subtract the terms

More Steps

Evaluate

- 54 x - 6 x

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

(- 54 - 6) x

Subtract the numbers

- 60 x

6 x^{3} - 27 x^{2} - 60 x

6 x^{3} - 27 x^{2} - 60 x - 3

Solution

3 (2 x^{3} - 9 x^{2} - 20 x - 1)

Show Solution

Find the roots

x_{1} \approx - 1.590325, x_{2} \approx - 0.051193, x_{3} \approx 6.141518

Evaluate

x^{2} \times 6 x - 27 x^{2} - 6 x \times 9 - 6 x - 3

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

x^{2} \times 6 x - 27 x^{2} - 6 x \times 9 - 6 x - 3 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

6 x^{3} - 27 x^{2} - 6 x \times 9 - 6 x - 3 = 0

Multiply the terms

6 x^{3} - 27 x^{2} - 54 x - 6 x - 3 = 0

Subtract the terms

More Steps

Simplify

6 x^{3} - 27 x^{2} - 54 x - 6 x

Subtract the terms

More Steps

Evaluate

- 54 x - 6 x

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

(- 54 - 6) x

Subtract the numbers

- 60 x

6 x^{3} - 27 x^{2} - 60 x

6 x^{3} - 27 x^{2} - 60 x - 3 = 0

Factor the expression

3 (2 x^{3} - 9 x^{2} - 20 x - 1) = 0

Divide both sides

2 x^{3} - 9 x^{2} - 20 x - 1 = 0

Calculate

x \approx 6.141518 x \approx - 1.590325 x \approx - 0.051193

Solution

x_{1} \approx - 1.590325, x_{2} \approx - 0.051193, x_{3} \approx 6.141518

Show Solution