Identify the coefficients $a$, $b$, and $c$ in the quadratic equation $3x^2-4x+7=0$, given the standard form $a{x}^2+bx+c=0$.

Factor the trinomial $x^2-7x+12$ completely.

Solve $(x+2)(3x-9)=0$ by applying the zero-product property.

Use the quadratic formula to solve for: $(x+2)(x+5)-14=0$.

A ball's height (in units of meters) after $t$ seconds is modeled by: $h\left(t\right)=-t^2+5t+6$. Find the time(s) when the ball is located at ground level where $h=0$.