Calculate: (3 x+2) (x-1) = 7-7 x

Expression: $$( 3 x + 2 ) ( x - 1 ) = 7 - 7 x$$

Use the distributive property to multiply $3x+2$ by $x-1$ and combine like terms.


Add $7x$ to both sides.


Combine $-x$ and $7x$ to get $6x$.


Add $2$ to both sides.


Add $7$ and $2$ to get $9$.


Divide both sides by $3$.


Dividing by $3$ undoes the multiplication by $3$.


Divide $6$ by $3$.


Divide $9$ by $3$.


Divide $2$, the coefficient of the $x$ term, by $2$ to get $1$. Then add the square of $1$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.


Square $1$.


Add $3$ to $1$.


Factor $x^{2}+2x+1$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.


Take the square root of both sides of the equation.



$$x+1=2$$ $$x+1=-2$$

Subtract $1$ from both sides of the equation.

$$x=1$$ $$x=-3$$