Solve (3x-8)(x 7)-x(x 7)

Question

Simplify the expression

14 x^{2} - 56 x

Evaluate

(3 x - 8) (x \times 7) - x (x \times 7)

Remove the parentheses

(3 x - 8) x \times 7 - x \times x \times 7

Multiply the terms

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Multiply the terms

(3 x - 8) x \times 7

Use the commutative property to reorder the terms

(3 x - 8) \times 7 x

Multiply the terms

7 x (3 x - 8)

7 x (3 x - 8) - x \times x \times 7

Multiply

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Multiply the terms

x \times x \times 7

Multiply the terms

x^{2} \times 7

Use the commutative property to reorder the terms

7 x^{2}

7 x (3 x - 8) - 7 x^{2}

Expand the expression

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Calculate

7 x (3 x - 8)

Apply the distributive property

7 x \times 3 x - 7 x \times 8

Multiply the terms

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Evaluate

7 x \times 3 x

Multiply the numbers

21 x \times x

Multiply the terms

21 x^{2}

21 x^{2} - 7 x \times 8

Multiply the numbers

21 x^{2} - 56 x

21 x^{2} - 56 x - 7 x^{2}

Solution

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Evaluate

21 x^{2} - 7 x^{2}

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

(21 - 7) x^{2}

Subtract the numbers

14 x^{2}

14 x^{2} - 56 x

Show Solution

Factor the expression

14 x (x - 4)

Evaluate

(3 x - 8) (x \times 7) - x (x \times 7)

Remove the parentheses

(3 x - 8) x \times 7 - x \times x \times 7

Use the commutative property to reorder the terms

(3 x - 8) \times 7 x - x \times x \times 7

Multiply the terms

7 x (3 x - 8) - x \times x \times 7

Use the commutative property to reorder the terms

7 x (3 x - 8) - x \times 7 x

Multiply the terms

More Steps

Evaluate

x \times 7 x

Use the commutative property to reorder the terms

7 x \times x

Multiply the terms

7 x^{2}

7 x (3 x - 8) - 7 x^{2}

Rewrite the expression

7 x (3 x - 8) - 7 x \times x

Factor out 7 x from the expression

7 x (3 x - 8 - x)

Factor the expression

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Evaluate

3 x - 8 - x

Subtract the terms

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Evaluate

3 x - x

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

(3 - 1) x

Subtract the numbers

2 x

2 x - 8

Factor the expression

2 (x - 4)

7 x \times 2 (x - 4)

Solution

14 x (x - 4)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 4

Evaluate

(3 x - 8) (x \times 7) - x (x \times 7)

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

(3 x - 8) (x \times 7) - x (x \times 7) = 0

Use the commutative property to reorder the terms

(3 x - 8) \times 7 x - x (x \times 7) = 0

Use the commutative property to reorder the terms

(3 x - 8) \times 7 x - x \times 7 x = 0

Multiply the terms

7 x (3 x - 8) - x \times 7 x = 0

Multiply the terms

More Steps

Evaluate

x \times 7 x

Use the commutative property to reorder the terms

7 x \times x

Multiply the terms

7 x^{2}

7 x (3 x - 8) - 7 x^{2} = 0

Calculate

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Evaluate

7 x (3 x - 8) - 7 x^{2}

Expand the expression

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Calculate

7 x (3 x - 8)

Apply the distributive property

7 x \times 3 x - 7 x \times 8

Multiply the terms

21 x^{2} - 7 x \times 8

Multiply the numbers

21 x^{2} - 56 x

21 x^{2} - 56 x - 7 x^{2}

Subtract the terms

More Steps

Evaluate

21 x^{2} - 7 x^{2}

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

(21 - 7) x^{2}

Subtract the numbers

14 x^{2}

14 x^{2} - 56 x

14 x^{2} - 56 x = 0

Factor the expression

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Evaluate

14 x^{2} - 56 x

Rewrite the expression

14 x \times x - 14 x \times 4

Factor out 14 x from the expression

14 x (x - 4)

14 x (x - 4) = 0

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

14 x = 0 x - 4 = 0

Solve the equation for x

x = 0 x - 4 = 0

Solve the equation for x

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Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 0 x = 4

Solution

x_{1} = 0, x_{2} = 4

Show Solution