Solve 3x - 2x(x - 1)

Question

Simplify the expression

5 x - 2 x^{2}

Evaluate

3 x - 2 x (x - 1)

Expand the expression

More Steps

Calculate

- 2 x (x - 1)

Apply the distributive property

- 2 x \times x - (- 2 x \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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^{2} + 2 x

3 x - 2 x^{2} + 2 x

Solution

More Steps

Evaluate

3 x + 2 x

Collect like terms by calculating the sum or difference of their coefficients

(3 + 2) x

Add the numbers

5 x

5 x - 2 x^{2}

Show Solution

Factor the expression

(5 - 2 x) x

Evaluate

3 x - 2 x (x - 1)

Rewrite the expression

3 x - 2 (x - 1) x

Factor out x from the expression

(3 - 2 (x - 1)) x

Solution

(5 - 2 x) x

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0, x_{2} = 2.5

Evaluate

3 x - 2 x (x - 1)

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

3 x - 2 x (x - 1) = 0

Calculate

More Steps

Evaluate

3 x - 2 x (x - 1)

Expand the expression

More Steps

Calculate

- 2 x (x - 1)

Apply the distributive property

- 2 x \times x - (- 2 x \times 1)

Multiply the terms

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

Any expression multiplied by 1 remains the same

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

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^{2} + 2 x

3 x - 2 x^{2} + 2 x

Add the terms

More Steps

Evaluate

3 x + 2 x

Collect like terms by calculating the sum or difference of their coefficients

(3 + 2) x

Add the numbers

5 x

5 x - 2 x^{2}

5 x - 2 x^{2} = 0

Factor the expression

More Steps

Evaluate

5 x - 2 x^{2}

Rewrite the expression

x \times 5 - x \times 2 x

Factor out x from the expression

x (5 - 2 x)

x (5 - 2 x) = 0

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

x = 0 5 - 2 x = 0

Solve the equation for x

More Steps

Evaluate

5 - 2 x = 0

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

- 2 x = 0 - 5

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

- 2 x = - 5

Change the signs on both sides of the equation

2 x = 5

Divide both sides

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

Divide the numbers

x = \frac{5}{2}

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

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 2.5

Show Solution