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

Question

Simplify the expression

4 x^{6} - 6 x^{5}

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

2 x^{5} \times 2 x

Multiply the numbers

4 x^{5} \times x

Multiply the terms

More Steps

Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

4 x^{6}

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

Solution

4 x^{6} - 6 x^{5}

Show Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1.5

Evaluate

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

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

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

Calculate

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

Multiply the terms

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

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

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 2 x - 3 = 0

Solve the equation

More Steps

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}

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 1.5

Show Solution