Solve 5(x-1)(x-4)

Question

Simplify the expression

5 x^{2} - 25 x + 20

Evaluate

5 (x - 1) (x - 4)

Multiply the terms

More Steps

Evaluate

5 (x - 1)

Apply the distributive property

5 x - 5 \times 1

Any expression multiplied by 1 remains the same

5 x - 5

(5 x - 5) (x - 4)

Apply the distributive property

5 x \times x - 5 x \times 4 - 5 x - (- 5 \times 4)

Multiply the terms

5 x^{2} - 5 x \times 4 - 5 x - (- 5 \times 4)

Multiply the numbers

5 x^{2} - 20 x - 5 x - (- 5 \times 4)

Multiply the numbers

5 x^{2} - 20 x - 5 x - (- 20)

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

5 x^{2} - 20 x - 5 x + 20

Solution

More Steps

Evaluate

- 20 x - 5 x

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

(- 20 - 5) x

Subtract the numbers

- 25 x

5 x^{2} - 25 x + 20

Show Solution

Find the roots

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

Evaluate

5 (x - 1) (x - 4)

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

5 (x - 1) (x - 4) = 0

Elimination the left coefficient

(x - 1) (x - 4) = 0

Separate the equation into 2 possible cases

x - 1 = 0 x - 4 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 x - 4 = 0

Solve the equation

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 = 1 x = 4

Solution

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

Show Solution