Solve -2(x-2)(3x-1)

Question

Simplify the expression

- 6 x^{2} + 14 x - 4

Evaluate

- 2 (x - 2) (3 x - 1)

Multiply the terms

More Steps

Evaluate

- 2 (x - 2)

Apply the distributive property

- 2 x - (- 2 \times 2)

Multiply the numbers

- 2 x - (- 4)

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 + 4

(- 2 x + 4) (3 x - 1)

Apply the distributive property

- 2 x \times 3 x - (- 2 x \times 1) + 4 \times 3 x - 4 \times 1

Multiply the terms

More Steps

Evaluate

- 2 x \times 3 x

Multiply the numbers

- 6 x \times x

Multiply the terms

- 6 x^{2}

- 6 x^{2} - (- 2 x \times 1) + 4 \times 3 x - 4 \times 1

Any expression multiplied by 1 remains the same

- 6 x^{2} - (- 2 x) + 4 \times 3 x - 4 \times 1

Multiply the numbers

- 6 x^{2} - (- 2 x) + 12 x - 4 \times 1

Any expression multiplied by 1 remains the same

- 6 x^{2} - (- 2 x) + 12 x - 4

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

- 6 x^{2} + 2 x + 12 x - 4

Solution

More Steps

Evaluate

2 x + 12 x

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

(2 + 12) x

Add the numbers

14 x

- 6 x^{2} + 14 x - 4

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

- 2 (x - 2) (3 x - 1)

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

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

Change the sign

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

x - 2 = 0 3 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 3 x - 1 = 0

Solve the equation

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}

x = 2 x = \frac{1}{3}

Solution

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

Alternative Form

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

Show Solution