Solve (3n-2)(2n-4)

Question

Simplify the expression

6 n^{2} - 16 n + 8

Evaluate

(3 n - 2) (2 n - 4)

Apply the distributive property

3 n \times 2 n - 3 n \times 4 - 2 \times 2 n - (- 2 \times 4)

Multiply the terms

More Steps

Evaluate

3 n \times 2 n

Multiply the numbers

6 n \times n

Multiply the terms

6 n^{2}

6 n^{2} - 3 n \times 4 - 2 \times 2 n - (- 2 \times 4)

Multiply the numbers

6 n^{2} - 12 n - 2 \times 2 n - (- 2 \times 4)

Multiply the numbers

6 n^{2} - 12 n - 4 n - (- 2 \times 4)

Multiply the numbers

6 n^{2} - 12 n - 4 n - (- 8)

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 n^{2} - 12 n - 4 n + 8

Solution

More Steps

Evaluate

- 12 n - 4 n

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

(- 12 - 4) n

Subtract the numbers

- 16 n

6 n^{2} - 16 n + 8

Show Solution

Factor the expression

2 (3 n - 2) (n - 2)

Evaluate

(3 n - 2) (2 n - 4)

Factor the expression

(3 n - 2) \times 2 (n - 2)

Solution

2 (3 n - 2) (n - 2)

Show Solution

Find the roots

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

Alternative Form

n_{1} = 0. \dot{6}, n_{2} = 2

Evaluate

(3 n - 2) (2 n - 4)

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

(3 n - 2) (2 n - 4) = 0

Separate the equation into 2 possible cases

3 n - 2 = 0 2 n - 4 = 0

Solve the equation

More Steps

Evaluate

3 n - 2 = 0

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

3 n = 0 + 2

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

3 n = 2

Divide both sides

\frac{3 n}{3} = \frac{2}{3}

Divide the numbers

n = \frac{2}{3}

n = \frac{2}{3} 2 n - 4 = 0

Solve the equation

More Steps

Evaluate

2 n - 4 = 0

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

2 n = 0 + 4

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

2 n = 4

Divide both sides

\frac{2 n}{2} = \frac{4}{2}

Divide the numbers

n = \frac{4}{2}

Divide the numbers

More Steps

Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

n = 2

n = \frac{2}{3} n = 2

Solution

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

Alternative Form

n_{1} = 0. \dot{6}, n_{2} = 2

Show Solution