# How do you solve -3x^3 + 7x^2 = 4?

The solutions are

${x}_{1} = 1 , {x}_{2} = 2 , {x}_{3} = - \frac{2}{3}$

#### Explanation:

We set $p \left(x\right) = - 3 {x}^{3} + 7 {x}^{2} - 4$ and we notice that

$p \left(1\right) = 0$ hence $x - 1$ factor of the polynomial .Also

$p \left(2\right) = 0$ hence $\left(x - 1\right) \left(x - 2\right)$ factor of the polynomial p(x).

It is easy to find now that $p \left(x\right) = \left(x - 1\right) \left(x - 2\right) \left(3 x + 2\right)$

Hence the solutions are

${x}_{1} = 1 , {x}_{2} = 2 , {x}_{3} = - \frac{2}{3}$