Answer
$g=-6, h=18$
$g=4,h=48$
Work Step by Step
$h=3g+36$ ............................................ eq(1)
$h=2g^2+7g-12$ ............................... eq (2)
From equation (1) and equation (2)
$2g^2+7g-12=3g+36$
$2g^2+7g-12-3g-36=0$
$2g^2+4g-48=0$
$g^2+2g-24=0$
$g^2+6g-4g-24=0$
$g(g+6)-4(g+6)=0$
$(g+6)(g-4)=0$
Now
$g+6=0$ $\Longrightarrow$ $g=-6$
Similarly
$g-4=0$ $\Longrightarrow$ $g=4$
Putting $g=-6$ in equation (1)
$h=3(-6)+36=18$
So $g=-6,h=18$ is a solution
Also put $g=4$ in equation (1)
$h=3(4)+36=48$ at $g=4$
So $g=4,h=48$ is a solution
CHECK
Putting $g=-6$,$h=18$ in equation (2)
$18=2(-6)^2+7(-6)-12$
$18=2(36)-54$
$18=72-54$
$18=18$
LHS=RHS
Similarly
Putting $g=4$,$h=48$ in equation (2)
$48=2(4)^2+7(4)-12$
$48=32+28-12$
$48=48$
