Solve (3x-2)(6x^2)-9(x^2-3x 1)

Question

Simplify the expression

18 x^{3} - 21 x^{2} + 27 x

Show Solution

3 x (6 x^{2} - 7 x + 9)

Show Solution

x_{1} = \frac{7}{12} - \frac{167}{12} i, x_{2} = \frac{7}{12} + \frac{167}{12} i, x_{3} = 0

Alternative Form

x_{1} \approx 0.58 \dot{3} - 1.076904 i, x_{2} \approx 0.58 \dot{3} + 1.076904 i, x_{3} = 0

Evaluate

(3 x - 2) (6 x^{2}) - 9 (x^{2} - 3 x \times 1)

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

(3 x - 2) (6 x^{2}) - 9 (x^{2} - 3 x \times 1) = 0

Multiply the terms

(3 x - 2) \times 6 x^{2} - 9 (x^{2} - 3 x \times 1) = 0

Multiply the terms

(3 x - 2) \times 6 x^{2} - 9 (x^{2} - 3 x) = 0

Multiply the terms

6 x^{2} (3 x - 2) - 9 (x^{2} - 3 x) = 0

Calculate

More Steps

18 x^{3} - 21 x^{2} + 27 x = 0

Factor the expression

3 x (6 x^{2} - 7 x + 9) = 0

Divide both sides

x (6 x^{2} - 7 x + 9) = 0

Separate the equation into 2 possible cases

x = 0 6 x^{2} - 7 x + 9 = 0

Solve the equation

More Steps

x = 0 x = \frac{7}{12} + \frac{167}{12} i x = \frac{7}{12} - \frac{167}{12} i

Solution

x_{1} = \frac{7}{12} - \frac{167}{12} i, x_{2} = \frac{7}{12} + \frac{167}{12} i, x_{3} = 0

Alternative Form

x_{1} \approx 0.58 \dot{3} - 1.076904 i, x_{2} \approx 0.58 \dot{3} + 1.076904 i, x_{3} = 0

Show Solution