Solve (3x-2)2-(x+6)2

Question

Simplify the expression

4 x - 16

Evaluate

(3 x - 2) \times 2 - (x + 6) \times 2

Multiply the terms

2 (3 x - 2) - (x + 6) \times 2

Multiply the terms

2 (3 x - 2) - 2 (x + 6)

Expand the expression

More Steps

Calculate

2 (3 x - 2)

Apply the distributive property

2 \times 3 x - 2 \times 2

Multiply the numbers

6 x - 2 \times 2

Multiply the numbers

6 x - 4

6 x - 4 - 2 (x + 6)

Expand the expression

More Steps

Calculate

- 2 (x + 6)

Apply the distributive property

- 2 x - 2 \times 6

Multiply the numbers

- 2 x - 12

6 x - 4 - 2 x - 12

Subtract the terms

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Evaluate

6 x - 2 x

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

(6 - 2) x

Subtract the numbers

4 x

4 x - 4 - 12

Solution

4 x - 16

Show Solution

Factor the expression

4 (x - 4)

Evaluate

(3 x - 2) \times 2 - (x + 6) \times 2

Multiply the terms

2 (3 x - 2) - (x + 6) \times 2

Multiply the terms

2 (3 x - 2) - 2 (x + 6)

Simplify

More Steps

Evaluate

2 (3 x - 2)

Apply the distributive property

2 \times 3 x + 2 (- 2)

Multiply the terms

6 x + 2 (- 2)

Multiply the terms

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Evaluate

2 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 2 \times 2

Multiply the numbers

- 4

6 x - 4

6 x - 4 - 2 (x + 6)

Simplify

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Evaluate

- 2 (x + 6)

Apply the distributive property

- 2 x - 2 \times 6

Multiply the terms

- 2 x - 12

6 x - 4 - 2 x - 12

Subtract the terms

More Steps

Evaluate

6 x - 2 x

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

(6 - 2) x

Subtract the numbers

4 x

4 x - 4 - 12

Subtract the numbers

4 x - 16

Solution

4 (x - 4)

Show Solution

Find the roots

x = 4

Evaluate

(3 x - 2) \times 2 - (x + 6) \times 2

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

(3 x - 2) \times 2 - (x + 6) \times 2 = 0

Multiply the terms

2 (3 x - 2) - (x + 6) \times 2 = 0

Multiply the terms

2 (3 x - 2) - 2 (x + 6) = 0

Calculate

More Steps

Evaluate

2 (3 x - 2) - 2 (x + 6)

Expand the expression

More Steps

Calculate

2 (3 x - 2)

Apply the distributive property

2 \times 3 x - 2 \times 2

Multiply the numbers

6 x - 2 \times 2

Multiply the numbers

6 x - 4

6 x - 4 - 2 (x + 6)

Expand the expression

More Steps

Calculate

- 2 (x + 6)

Apply the distributive property

- 2 x - 2 \times 6

Multiply the numbers

- 2 x - 12

6 x - 4 - 2 x - 12

Subtract the terms

More Steps

Evaluate

6 x - 2 x

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

(6 - 2) x

Subtract the numbers

4 x

4 x - 4 - 12

Subtract the numbers

4 x - 16

4 x - 16 = 0

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

4 x = 0 + 16

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

4 x = 16

Divide both sides

\frac{4 x}{4} = \frac{16}{4}

Divide the numbers

x = \frac{16}{4}

Solution

More Steps

Evaluate

\frac{16}{4}

Reduce the numbers

\frac{4}{1}

Calculate

4

x = 4

Show Solution