Solve (x-3)(3x-3)=9

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Evaluate

(x - 3) (3 x - 3) = 9

Expand the expression

More Steps

Evaluate

(x - 3) (3 x - 3)

Apply the distributive property

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

Multiply the terms

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Evaluate

x \times 3 x

Use the commutative property to reorder the terms

3 x \times x

Multiply the terms

3 x^{2}

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

Use the commutative property to reorder the terms

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

Multiply the numbers

3 x^{2} - 3 x - 9 x - (- 3 \times 3)

Multiply the numbers

3 x^{2} - 3 x - 9 x - (- 9)

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

3 x^{2} - 3 x - 9 x + 9

Subtract the terms

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Evaluate

- 3 x - 9 x

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

(- 3 - 9) x

Subtract the numbers

- 12 x

3 x^{2} - 12 x + 9

3 x^{2} - 12 x + 9 = 9

Move the expression to the left side

3 x^{2} - 12 x = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 12 x

Rewrite the expression

3 x \times x - 3 x \times 4

Factor out 3 x from the expression

3 x (x - 4)

3 x (x - 4) = 0

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

x - 4 = 0 3 x = 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 = 4 3 x = 0

Solve the equation for x

x = 4 x = 0

Solution

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

Show Solution

Solve the quadratic equation

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