Solve 2(x-2) x=3(x-1)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{1}{2}, x_{2} = 3

Alternative Form

x_{1} = 0.5, x_{2} = 3

Evaluate

2 (x - 2) x = 3 (x - 1)

Multiply the terms

2 x (x - 2) = 3 (x - 1)

Expand the expression

More Steps

Evaluate

2 x (x - 2)

Apply the distributive property

2 x \times x - 2 x \times 2

Multiply the terms

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

Multiply the numbers

2 x^{2} - 4 x

2 x^{2} - 4 x = 3 (x - 1)

Expand the expression

More Steps

Evaluate

3 (x - 1)

Apply the distributive property

3 x - 3 \times 1

Any expression multiplied by 1 remains the same

3 x - 3

2 x^{2} - 4 x = 3 x - 3

Move the expression to the left side

2 x^{2} - 7 x + 3 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 7 x + 3

Rewrite the expression

2 x^{2} + (- 1 - 6) x + 3

Calculate

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

Rewrite the expression

x \times 2 x - x - 3 \times 2 x + 3

Factor out x from the expression

x (2 x - 1) - 3 \times 2 x + 3

Factor out - 3 from the expression

x (2 x - 1) - 3 (2 x - 1)

Factor out 2 x - 1 from the expression

(x - 3) (2 x - 1)

(x - 3) (2 x - 1) = 0

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

x - 3 = 0 2 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 2 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 3 x = \frac{1}{2}

Solution

x_{1} = \frac{1}{2}, x_{2} = 3

Alternative Form

x_{1} = 0.5, x_{2} = 3

Show Solution