Use factorisation to solve the equation. $2h^2 - 11h - 21 = 0$ Answer h = ... or ...

1. Factorise the quadratic expression.

$2h^2-11h-21=0$

Find two numbers with product $2(-21)=-42$ and sum $-11$: $-14$ and $3$.

$2h^2-14h+3h-21=0$
$2h(h-7)+3(h-7)=0$
$(2h+3)(h-7)=0$

2. Set each factor equal to zero and solve for $h$.

$(2h+3)(h-7)=0$

So,
$2h+3=0 \quad \text{or} \quad h-7=0$

$h=-\dfrac{3}{2} \quad \text{or} \quad h=7$