Solve 3x^2 2x - 6

Question

Simplify the expression

6 x^{3} - 6

Evaluate

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

Solution

More Steps

Evaluate

3 x^{2} \times 2 x

Multiply the terms

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

6 x^{3} - 6

Show Solution

6 (x - 1) (x^{2} + x + 1)

Evaluate

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

Evaluate

More Steps

Evaluate

3 x^{2} \times 2 x

Multiply the terms

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

6 x^{3} - 6

Factor out 6 from the expression

6 (x^{3} - 1)

Solution

More Steps

Evaluate

x^{3} - 1

Rewrite the expression in exponential form

x^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

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

Any expression multiplied by 1 remains the same

(x - 1) (x^{2} + x + 1^{2})

1 raised to any power equals to 1

(x - 1) (x^{2} + x + 1)

6 (x - 1) (x^{2} + x + 1)

Show Solution

x = 1

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

3 x^{2} \times 2 x

Multiply the terms

6 x^{2} \times x

Multiply the terms with the same base by adding their exponents

6 x^{2 + 1}

Add the numbers

6 x^{3}

6 x^{3} - 6 = 0

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

6 x^{3} = 0 + 6

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

6 x^{3} = 6

Divide both sides

\frac{6 x ^{3}}{6} = \frac{6}{6}

Divide the numbers

x^{3} = \frac{6}{6}

Divide the numbers

More Steps

Evaluate

\frac{6}{6}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{3} = 1

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

3 x^{3} = 31

Calculate

x = 31

Solution

x = 1

Show Solution