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

Question

Simplify the expression

24 x^{2} - 54 x + 12

Evaluate

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

Multiply the terms

6 (x - 2) (4 x - 1)

Multiply the terms

More Steps

Evaluate

6 (x - 2)

Apply the distributive property

6 x - 6 \times 2

Multiply the numbers

6 x - 12

(6 x - 12) (4 x - 1)

Apply the distributive property

6 x \times 4 x - 6 x \times 1 - 12 \times 4 x - (- 12 \times 1)

Multiply the terms

More Steps

Evaluate

6 x \times 4 x

Multiply the numbers

24 x \times x

Multiply the terms

24 x^{2}

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

Any expression multiplied by 1 remains the same

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

Multiply the numbers

24 x^{2} - 6 x - 48 x - (- 12 \times 1)

Any expression multiplied by 1 remains the same

24 x^{2} - 6 x - 48 x - (- 12)

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

24 x^{2} - 6 x - 48 x + 12

Solution

More Steps

Evaluate

- 6 x - 48 x

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

(- 6 - 48) x

Subtract the numbers

- 54 x

24 x^{2} - 54 x + 12

Show Solution

Find the roots

x_{1} = \frac{1}{4}, x_{2} = 2

Alternative Form

x_{1} = 0.25, x_{2} = 2

Evaluate

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

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

3 (x - 2) \times 2 (4 x - 1) = 0

Multiply the terms

6 (x - 2) (4 x - 1) = 0

Elimination the left coefficient

(x - 2) (4 x - 1) = 0

Separate the equation into 2 possible cases

x - 2 = 0 4 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 4 x - 1 = 0

Solve the equation

More Steps

Evaluate

4 x - 1 = 0

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

4 x = 0 + 1

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

4 x = 1

Divide both sides

\frac{4 x}{4} = \frac{1}{4}

Divide the numbers

x = \frac{1}{4}

x = 2 x = \frac{1}{4}

Solution

x_{1} = \frac{1}{4}, x_{2} = 2

Alternative Form

x_{1} = 0.25, x_{2} = 2

Show Solution