Solve (x - 4)(2x^23x - 5)

Question

Simplify the expression

6 x^{4} - 5 x - 24 x^{3} + 20

Evaluate

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

Multiply

More Steps

Evaluate

2 x^{2} \times 3 x

Multiply the terms

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

(x - 4) (6 x^{3} - 5)

Apply the distributive property

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

Multiply the terms

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Evaluate

x \times 6 x^{3}

Use the commutative property to reorder the terms

6 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

6 x^{4}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

6 x^{4} - 5 x - 24 x^{3} - (- 4 \times 5)

Multiply the numbers

6 x^{4} - 5 x - 24 x^{3} - (- 20)

Solution

6 x^{4} - 5 x - 24 x^{3} + 20

Show Solution

Find the roots

x_{1} = \frac{3 180}{6}, x_{2} = 4

Alternative Form

x_{1} \approx 0.941036, x_{2} = 4

Evaluate

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

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

(x - 4) (2 x^{2} \times 3 x - 5) = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times 3 x

Multiply the terms

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

(x - 4) (6 x^{3} - 5) = 0

Separate the equation into 2 possible cases

x - 4 = 0 6 x^{3} - 5 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 4 6 x^{3} - 5 = 0

Solve the equation

More Steps

Evaluate

6 x^{3} - 5 = 0

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

6 x^{3} = 0 + 5

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

6 x^{3} = 5

Divide both sides

\frac{6 x ^{3}}{6} = \frac{5}{6}

Divide the numbers

x^{3} = \frac{5}{6}

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

3 x^{3} = 3 \frac{5}{6}

Calculate

x = 3 \frac{5}{6}

Simplify the root

More Steps

Evaluate

3 \frac{5}{6}

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

\frac{3 5}{3 6}

Multiply by the Conjugate

\frac{3 5 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 5 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 180}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 180}{6}

x = \frac{3 180}{6}

x = 4 x = \frac{3 180}{6}

Solution

x_{1} = \frac{3 180}{6}, x_{2} = 4

Alternative Form

x_{1} \approx 0.941036, x_{2} = 4

Show Solution