Solve (x^23x - 9) (4x^2 - 6x 1)

Question

Simplify the expression

12 x^{5} - 18 x^{4} - 36 x^{2} + 54 x

Evaluate

(x^{2} \times 3 x - 9) (4 x^{2} - 6 x \times 1)

Multiply

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Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(3 x^{3} - 9) (4 x^{2} - 6 x \times 1)

Multiply the terms

(3 x^{3} - 9) (4 x^{2} - 6 x)

Apply the distributive property

3 x^{3} \times 4 x^{2} - 3 x^{3} \times 6 x - 9 \times 4 x^{2} - (- 9 \times 6 x)

Multiply the terms

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Evaluate

3 x^{3} \times 4 x^{2}

Multiply the numbers

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

Multiply the terms

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Evaluate

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

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 2}

Add the numbers

x^{5}

12 x^{5}

12 x^{5} - 3 x^{3} \times 6 x - 9 \times 4 x^{2} - (- 9 \times 6 x)

Multiply the terms

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Evaluate

3 x^{3} \times 6 x

Multiply the numbers

18 x^{3} \times x

Multiply the terms

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Evaluate

x^{3} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 1}

Add the numbers

x^{4}

18 x^{4}

12 x^{5} - 18 x^{4} - 9 \times 4 x^{2} - (- 9 \times 6 x)

Multiply the numbers

12 x^{5} - 18 x^{4} - 36 x^{2} - (- 9 \times 6 x)

Multiply the numbers

12 x^{5} - 18 x^{4} - 36 x^{2} - (- 54 x)

Solution

12 x^{5} - 18 x^{4} - 36 x^{2} + 54 x

Show Solution

Factor the expression

6 x (x^{3} - 3) (2 x - 3)

Evaluate

(x^{2} \times 3 x - 9) (4 x^{2} - 6 x \times 1)

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(3 x^{3} - 9) (4 x^{2} - 6 x \times 1)

Multiply the terms

(3 x^{3} - 9) (4 x^{2} - 6 x)

Factor the expression

3 (x^{3} - 3) (4 x^{2} - 6 x)

Factor the expression

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Evaluate

4 x^{2} - 6 x

Rewrite the expression

2 x \times 2 x - 2 x \times 3

Factor out 2 x from the expression

2 x (2 x - 3)

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

Solution

6 x (x^{3} - 3) (2 x - 3)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 33, x_{3} = \frac{3}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.44225, x_{3} = 1.5

Evaluate

(x^{2} \times 3 x - 9) (4 x^{2} - 6 x \times 1)

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

(x^{2} \times 3 x - 9) (4 x^{2} - 6 x \times 1) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

(3 x^{3} - 9) (4 x^{2} - 6 x \times 1) = 0

Multiply the terms

(3 x^{3} - 9) (4 x^{2} - 6 x) = 0

Separate the equation into 2 possible cases

3 x^{3} - 9 = 0 4 x^{2} - 6 x = 0

Solve the equation

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Evaluate

3 x^{3} - 9 = 0

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

3 x^{3} = 0 + 9

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

3 x^{3} = 9

Divide both sides

\frac{3 x ^{3}}{3} = \frac{9}{3}

Divide the numbers

x^{3} = \frac{9}{3}

Divide the numbers

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Evaluate

\frac{9}{3}

Reduce the numbers

\frac{3}{1}

Calculate

3

x^{3} = 3

Take the 3 -th root on both sides of the equation

3 x^{3} = 33

Calculate

x = 33

x = 33 4 x^{2} - 6 x = 0

Solve the equation

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Evaluate

4 x^{2} - 6 x = 0

Factor the expression

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Evaluate

4 x^{2} - 6 x

Rewrite the expression

2 x \times 2 x - 2 x \times 3

Factor out 2 x from the expression

2 x (2 x - 3)

2 x (2 x - 3) = 0

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

2 x = 0 2 x - 3 = 0

Solve the equation for x

x = 0 2 x - 3 = 0

Solve the equation for x

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Evaluate

2 x - 3 = 0

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

2 x = 0 + 3

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

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = 0 x = \frac{3}{2}

x = 33 x = 0 x = \frac{3}{2}

Solution

x_{1} = 0, x_{2} = 33, x_{3} = \frac{3}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.44225, x_{3} = 1.5

Show Solution