Solve 6x^35x^2-12x^4

Question

Simplify the expression

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

Evaluate

6 x^{3} \times 5 x^{2} - 12 x^{4}

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

30 x^{3 + 2}

Add the numbers

30 x^{5}

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

Show Solution

6 x^{4} (5 x - 2)

Evaluate

6 x^{3} \times 5 x^{2} - 12 x^{4}

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

30 x^{3 + 2}

Add the numbers

30 x^{5}

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

Rewrite the expression

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

Solution

6 x^{4} (5 x - 2)

Show Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0.4

Evaluate

6 x^{3} \times 5 x^{2} - 12 x^{4}

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

6 x^{3} \times 5 x^{2} - 12 x^{4} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

30 x^{3 + 2}

Add the numbers

30 x^{5}

30 x^{5} - 12 x^{4} = 0

Factor the expression

6 x^{4} (5 x - 2) = 0

Divide both sides

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

Separate the equation into 2 possible cases

x^{4} = 0 5 x - 2 = 0

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

x = 0 5 x - 2 = 0

Solve the equation

More Steps

Evaluate

5 x - 2 = 0

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

5 x = 0 + 2

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

5 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{5}

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

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0.4

Show Solution