Solve (3x^2)-(x-8) 7x

Question

Simplify the expression

- 4 x^{2} + 56 x

Evaluate

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

Multiply the first two terms

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

Expand the expression

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Calculate

- 7 (x - 8) x

Simplify

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Evaluate

- 7 (x - 8)

Apply the distributive property

- 7 x - (- 7 \times 8)

Multiply the numbers

- 7 x - (- 56)

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

- 7 x + 56

(- 7 x + 56) x

Apply the distributive property

- 7 x \times x + 56 x

Multiply the terms

- 7 x^{2} + 56 x

3 x^{2} - 7 x^{2} + 56 x

Solution

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Evaluate

3 x^{2} - 7 x^{2}

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

(3 - 7) x^{2}

Subtract the numbers

- 4 x^{2}

- 4 x^{2} + 56 x

Show Solution

Factor the expression

- 4 x (x - 14)

Evaluate

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

Multiply the terms

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Evaluate

(x - 8) \times 7 x

Multiply the first two terms

7 (x - 8) x

Multiply the terms

7 x (x - 8)

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

Rewrite the expression

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

Factor out x from the expression

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

Factor the expression

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Evaluate

3 x - 7 (x - 8)

Simplify

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Evaluate

- 7 (x - 8)

Apply the distributive property

- 7 x - 7 (- 8)

Multiply the terms

- 7 x + 56

3 x - 7 x + 56

Subtract the terms

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Evaluate

3 x - 7 x

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

(3 - 7) x

Subtract the numbers

- 4 x

- 4 x + 56

Factor the expression

- 4 (x - 14)

- 4 (x - 14) x

Solution

- 4 x (x - 14)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 14

Evaluate

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

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

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

Multiply the terms

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

Multiply the first two terms

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

Calculate

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Evaluate

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

Expand the expression

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Calculate

- 7 (x - 8) x

Simplify

(- 7 x + 56) x

Apply the distributive property

- 7 x \times x + 56 x

Multiply the terms

- 7 x^{2} + 56 x

3 x^{2} - 7 x^{2} + 56 x

Subtract the terms

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Evaluate

3 x^{2} - 7 x^{2}

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

(3 - 7) x^{2}

Subtract the numbers

- 4 x^{2}

- 4 x^{2} + 56 x

- 4 x^{2} + 56 x = 0

Factor the expression

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Evaluate

- 4 x^{2} + 56 x

Rewrite the expression

- 4 x \times x + 4 x \times 14

Factor out - 4 x from the expression

- 4 x (x - 14)

- 4 x (x - 14) = 0

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

- 4 x = 0 x - 14 = 0

Solve the equation for x

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Evaluate

- 4 x = 0

Change the signs on both sides of the equation

4 x = 0

Rewrite the expression

x = 0

x = 0 x - 14 = 0

Solve the equation for x

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Evaluate

x - 14 = 0

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

x = 0 + 14

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

x = 14

x = 0 x = 14

Solution

x_{1} = 0, x_{2} = 14

Show Solution