Answer
The solutions are -2 and $\frac{7}{3}$.
Work Step by Step
x(3x-1)=14
3$x^{2}$-x=14
3$x^{2}$-x-14=14-14
3$x^{2}$-x-14=0
3$x^{2}$-7x+6x-14=0
x(3x-7)+2(3x-7)=0
(x+2)(3x-7)=0
x+2=0 3x-7=0
x+2-2=0-2 or 3 x-7+7=0+7
x=-2 or 3 x=7
x=-2 or $\frac{3x}{3}$=$\frac{7}{3}$
x=-2 or x=$\frac{7}{3}$
The solutions are -2 and $\frac{7}{3}$.
Check
Let x=-2
x(3x-1)=14
-2[3(-2)-1]=14
-2[-6-1]=14
-2[-7]=14
14=14
Let x=$\frac{7}{3}$
x(3x-1)=14
$\frac{7}{3}$(3$\frac{7}{3}$-1)=14
$\frac{7}{3}$(7-1)=14
$\frac{7}{3}$(7-1)=14
$\frac{7}{3}$*6=14
$\frac{42}{3}$=14
14=14
