Solve 4x^3(2x-5) 6(1-5x)

Question

Simplify the expression

648 x^{4} - 240 x^{5} - 120 x^{3}

Evaluate

4 x^{3} (2 x - 5) \times 6 (1 - 5 x)

Multiply the terms

24 x^{3} (2 x - 5) (1 - 5 x)

Multiply the terms

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Evaluate

24 x^{3} (2 x - 5)

Apply the distributive property

24 x^{3} \times 2 x - 24 x^{3} \times 5

Multiply the terms

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Evaluate

24 x^{3} \times 2 x

Multiply the numbers

48 x^{3} \times x

Multiply the terms

48 x^{4}

48 x^{4} - 24 x^{3} \times 5

Multiply the numbers

48 x^{4} - 120 x^{3}

(48 x^{4} - 120 x^{3}) (1 - 5 x)

Apply the distributive property

48 x^{4} \times 1 - 48 x^{4} \times 5 x - 120 x^{3} \times 1 - (- 120 x^{3} \times 5 x)

Any expression multiplied by 1 remains the same

48 x^{4} - 48 x^{4} \times 5 x - 120 x^{3} \times 1 - (- 120 x^{3} \times 5 x)

Multiply the terms

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Evaluate

48 x^{4} \times 5 x

Multiply the numbers

240 x^{4} \times x

Multiply the terms

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Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

240 x^{5}

48 x^{4} - 240 x^{5} - 120 x^{3} \times 1 - (- 120 x^{3} \times 5 x)

Any expression multiplied by 1 remains the same

48 x^{4} - 240 x^{5} - 120 x^{3} - (- 120 x^{3} \times 5 x)

Multiply the terms

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Evaluate

- 120 x^{3} \times 5 x

Multiply the numbers

- 600 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}

- 600 x^{4}

48 x^{4} - 240 x^{5} - 120 x^{3} - (- 600 x^{4})

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

48 x^{4} - 240 x^{5} - 120 x^{3} + 600 x^{4}

Solution

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Evaluate

48 x^{4} + 600 x^{4}

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

(48 + 600) x^{4}

Add the numbers

648 x^{4}

648 x^{4} - 240 x^{5} - 120 x^{3}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{5}, x_{3} = \frac{5}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.2, x_{3} = 2.5

Evaluate

4 x^{3} (2 x - 5) \times 6 (1 - 5 x)

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

4 x^{3} (2 x - 5) \times 6 (1 - 5 x) = 0

Multiply the terms

24 x^{3} (2 x - 5) (1 - 5 x) = 0

Elimination the left coefficient

x^{3} (2 x - 5) (1 - 5 x) = 0

Separate the equation into 3 possible cases

x^{3} = 0 2 x - 5 = 0 1 - 5 x = 0

The only way a power can be 0 is when the base equals 0

x = 0 2 x - 5 = 0 1 - 5 x = 0

Solve the equation

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Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

\frac{2 x}{2} = \frac{5}{2}

Divide the numbers

x = \frac{5}{2}

x = 0 x = \frac{5}{2} 1 - 5 x = 0

Solve the equation

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Evaluate

1 - 5 x = 0

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

- 5 x = 0 - 1

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

- 5 x = - 1

Change the signs on both sides of the equation

5 x = 1

Divide both sides

\frac{5 x}{5} = \frac{1}{5}

Divide the numbers

x = \frac{1}{5}

x = 0 x = \frac{5}{2} x = \frac{1}{5}

Solution

x_{1} = 0, x_{2} = \frac{1}{5}, x_{3} = \frac{5}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.2, x_{3} = 2.5

Show Solution