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

Question

Simplify the expression

2 x^{2} - 2 x

Evaluate

2 x \times x - 2 (x - 3) - 6

Multiply the terms

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

Expand the expression

More Steps

Calculate

- 2 (x - 3)

Apply the distributive property

- 2 x - (- 2 \times 3)

Multiply the numbers

- 2 x - (- 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 2 x + 6

2 x^{2} - 2 x + 6 - 6

Solution

2 x^{2} - 2 x

Show Solution

Factor the expression

2 x (x - 1)

Evaluate

2 x \times x - 2 (x - 3) - 6

Multiply the terms

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

Subtract the terms

More Steps

Evaluate

- 2 (x - 3) - 6

Rewrite the expression

(- x + 3) \times 2 - 3 \times 2

Factor the expression

(- x + 3 - 3) \times 2

Since two opposites add up to 0,remove them form the expression

- x \times 2

Use the commutative property to reorder the terms

- 2 x

2 x^{2} - 2 x

Rewrite the expression

2 x \times x - 2 x

Solution

2 x (x - 1)

Show Solution

Find the roots

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

Evaluate

2 x \times x - 2 (x - 3) - 6

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

2 x \times x - 2 (x - 3) - 6 = 0

Multiply the terms

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

Expand the expression

More Steps

Simplify

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

Expand the expression

More Steps

Evaluate

- 2 (x - 3)

Apply the distributive property

- 2 x - (- 2 \times 3)

Multiply the numbers

- 2 x - (- 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 2 x + 6

2 x^{2} - 2 x + 6

2 x^{2} - 2 x + 6 - 6 = 0

Since two opposites add up to 0,remove them form the expression

2 x^{2} - 2 x = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 2 x

Rewrite the expression

2 x \times x - 2 x

Factor out 2 x from the expression

2 x (x - 1)

2 x (x - 1) = 0

When the product of factors equals 0,at least one factor is 0

2 x = 0 x - 1 = 0

Solve the equation for x

x = 0 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1

Solution

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

Show Solution