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

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 0, x_{2} = 5

Evaluate

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

Expand the expression

More Steps

Evaluate

(x - 2) (x - 3)

Apply the distributive property

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the numbers

x^{2} - 3 x - 2 x - (- 6)

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

x^{2} - 3 x - 2 x + 6

Subtract the terms

More Steps

Evaluate

- 3 x - 2 x

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

(- 3 - 2) x

Subtract the numbers

- 5 x

x^{2} - 5 x + 6

x^{2} - 5 x + 6 = 6

Move the expression to the left side

x^{2} - 5 x = 0

Factor the expression

More Steps

Evaluate

x^{2} - 5 x

Rewrite the expression

x \times x - x \times 5

Factor out x from the expression

x (x - 5)

x (x - 5) = 0

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

x - 5 = 0 x = 0

Solve the equation for x

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 5 x = 0

Solution

x_{1} = 0, x_{2} = 5

Show Solution

Solve the quadratic equation

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