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

Question

Solve the equation

x_{1} = 0, x_{2} \approx 0.082506, x_{3} \approx 2.5828

Evaluate

(x^{2} - 2 x)^{2} \times 3 (x - 1) = x (2 x - 1)

Use the commutative property to reorder the terms

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

Calculate

More Steps

3 x^{5} - 15 x^{4} + 24 x^{3} - 12 x^{2} = x (2 x - 1)

Calculate

More Steps

3 x^{5} - 15 x^{4} + 24 x^{3} - 12 x^{2} = 2 x^{2} - x

Move the expression to the left side

3 x^{5} - 15 x^{4} + 24 x^{3} - 12 x^{2} - (2 x^{2} - x) = 0

Calculate the sum or difference

More Steps

3 x^{5} - 15 x^{4} + 24 x^{3} - 14 x^{2} + x = 0

Factor the expression

x (3 x^{4} - 15 x^{3} + 24 x^{2} - 14 x + 1) = 0

Separate the equation into 2 possible cases

x = 0 3 x^{4} - 15 x^{3} + 24 x^{2} - 14 x + 1 = 0

Solve the equation

x = 0 x \approx 2.5828 x \approx 0.082506

Solution

x_{1} = 0, x_{2} \approx 0.082506, x_{3} \approx 2.5828

Show Solution