Solve (3x^2-5x) - (9x^2-3x)

Question

Simplify the expression

- 6 x^{2} - 2 x

Evaluate

(3 x^{2} - 5 x) - (9 x^{2} - 3 x)

Remove the parentheses

3 x^{2} - 5 x - (9 x^{2} - 3 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

3 x^{2} - 5 x - 9 x^{2} + 3 x

Subtract the terms

More Steps

Evaluate

3 x^{2} - 9 x^{2}

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

(3 - 9) x^{2}

Subtract the numbers

- 6 x^{2}

- 6 x^{2} - 5 x + 3 x

Solution

More Steps

Evaluate

- 5 x + 3 x

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

(- 5 + 3) x

Add the numbers

- 2 x

- 6 x^{2} - 2 x

Show Solution

Factor the expression

- 2 x (3 x + 1)

Evaluate

(3 x^{2} - 5 x) - (9 x^{2} - 3 x)

Remove the parentheses

3 x^{2} - 5 x - (9 x^{2} - 3 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

3 x^{2} - 5 x - 9 x^{2} + 3 x

Subtract the terms

More Steps

Evaluate

3 x^{2} - 9 x^{2}

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

(3 - 9) x^{2}

Subtract the numbers

- 6 x^{2}

- 6 x^{2} - 5 x + 3 x

Add the terms

More Steps

Evaluate

- 5 x + 3 x

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

(- 5 + 3) x

Add the numbers

- 2 x

- 6 x^{2} - 2 x

Rewrite the expression

- 2 x \times 3 x - 2 x

Solution

- 2 x (3 x + 1)

Show Solution

Find the roots

x_{1} = - \frac{1}{3}, x_{2} = 0

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0

Evaluate

(3 x^{2} - 5 x) - (9 x^{2} - 3 x)

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

(3 x^{2} - 5 x) - (9 x^{2} - 3 x) = 0

Remove the parentheses

3 x^{2} - 5 x - (9 x^{2} - 3 x) = 0

Subtract the terms

More Steps

Simplify

3 x^{2} - 5 x - (9 x^{2} - 3 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

3 x^{2} - 5 x - 9 x^{2} + 3 x

Subtract the terms

More Steps

Evaluate

3 x^{2} - 9 x^{2}

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

(3 - 9) x^{2}

Subtract the numbers

- 6 x^{2}

- 6 x^{2} - 5 x + 3 x

Add the terms

More Steps

Evaluate

- 5 x + 3 x

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

(- 5 + 3) x

Add the numbers

- 2 x

- 6 x^{2} - 2 x

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

Factor the expression

More Steps

Evaluate

- 6 x^{2} - 2 x

Rewrite the expression

- 2 x \times 3 x - 2 x

Factor out - 2 x from the expression

- 2 x (3 x + 1)

- 2 x (3 x + 1) = 0

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

- 2 x = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

- 2 x = 0

Change the signs on both sides of the equation

2 x = 0

Rewrite the expression

x = 0

x = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 1 = 0

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

3 x = 0 - 1

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

3 x = - 1

Divide both sides

\frac{3 x}{3} = \frac{- 1}{3}

Divide the numbers

x = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{3}

x = 0 x = - \frac{1}{3}

Solution

x_{1} = - \frac{1}{3}, x_{2} = 0

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0

Show Solution