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

Question

Simplify the expression

6 x^{5} - 12 x^{4}

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{1 + 3} (x - 2) \times 2 \times 3

Add the numbers

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

Multiply the terms

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

Use the commutative property to reorder the terms

6 x^{4} (x - 2)

Apply the distributive property

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

Multiply the terms

More Steps

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}

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

Solution

6 x^{5} - 12 x^{4}

Show Solution

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

Evaluate

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

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

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

Calculate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{1 + 3} (x - 2) \times 2 \times 3

Add the numbers

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

Multiply the terms

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

Use the commutative property to reorder the terms

6 x^{4} (x - 2)

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

Elimination the left coefficient

x^{4} (x - 2) = 0

Separate the equation into 2 possible cases

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

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

x = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 2

Solution

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

Show Solution