Solve 5x(x-1) - 15x(1-)

Question

Simplify the expression

5 x^{2} - 20 x

Evaluate

5 x (x - 1) - 15 x \times 1

Multiply the terms

5 x (x - 1) - 15 x

Expand the expression

More Steps

Calculate

5 x (x - 1)

Apply the distributive property

5 x \times x - 5 x \times 1

Multiply the terms

5 x^{2} - 5 x \times 1

Any expression multiplied by 1 remains the same

5 x^{2} - 5 x

5 x^{2} - 5 x - 15 x

Solution

More Steps

Evaluate

- 5 x - 15 x

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

(- 5 - 15) x

Subtract the numbers

- 20 x

5 x^{2} - 20 x

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Factor the expression

5 x (x - 4)

Evaluate

5 x (x - 1) - 15 x \times 1

Multiply the terms

5 x (x - 1) - 15 x

Rewrite the expression

5 x (x - 1) - 5 x \times 3

Factor out 5 x from the expression

5 x (x - 1 - 3)

Solution

5 x (x - 4)

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Find the roots

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

Evaluate

5 x (x - 1) - 15 x \times 1

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

5 x (x - 1) - 15 x \times 1 = 0

Multiply the terms

5 x (x - 1) - 15 x = 0

Calculate

More Steps

Evaluate

5 x (x - 1) - 15 x

Expand the expression

More Steps

Calculate

5 x (x - 1)

Apply the distributive property

5 x \times x - 5 x \times 1

Multiply the terms

5 x^{2} - 5 x \times 1

Any expression multiplied by 1 remains the same

5 x^{2} - 5 x

5 x^{2} - 5 x - 15 x

Subtract the terms

More Steps

Evaluate

- 5 x - 15 x

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

(- 5 - 15) x

Subtract the numbers

- 20 x

5 x^{2} - 20 x

5 x^{2} - 20 x = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 20 x

Rewrite the expression

5 x \times x - 5 x \times 4

Factor out 5 x from the expression

5 x (x - 4)

5 x (x - 4) = 0

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

5 x = 0 x - 4 = 0

Solve the equation for x

x = 0 x - 4 = 0

Solve the equation for x

More Steps

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