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

Question

Simplify the expression

6 x^{5} - 15 x^{2}

Evaluate

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

Subtract the terms

More Steps

Simplify

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

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

(6 - 3) x^{2}

Subtract the numbers

3 x^{2}

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

Multiply

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Multiply the terms

2 x^{2} \times x

Multiply the terms with the same base by adding their exponents

2 x^{2 + 1}

Add the numbers

2 x^{3}

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

Apply the distributive property

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

Multiply the terms

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Evaluate

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

Multiply the numbers

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

Multiply the terms

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Evaluate

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

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

x^{2 + 3}

Add the numbers

x^{5}

6 x^{5}

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

Solution

6 x^{5} - 15 x^{2}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 20}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.357209

Evaluate

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

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

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

Subtract the terms

More Steps

Simplify

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

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

(6 - 3) x^{2}

Subtract the numbers

3 x^{2}

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

Multiply

More Steps

Multiply the terms

2 x^{2} \times x

Multiply the terms with the same base by adding their exponents

2 x^{2 + 1}

Add the numbers

2 x^{3}

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

2 x^{3} - 5 = 0

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

2 x^{3} = 0 + 5

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

2 x^{3} = 5

Divide both sides

\frac{2 x ^{3}}{2} = \frac{5}{2}

Divide the numbers

x^{3} = \frac{5}{2}

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

3 x^{3} = 3 \frac{5}{2}

Calculate

x = 3 \frac{5}{2}

Simplify the root

More Steps

Evaluate

3 \frac{5}{2}

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

\frac{3 5}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 5 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 20}{3 2 \times 3 2 ^{2}}

Multiply the numbers

\frac{3 20}{2}

x = \frac{3 20}{2}

x = 0 x = \frac{3 20}{2}

Solution

x_{1} = 0, x_{2} = \frac{3 20}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 1.357209

Show Solution