1. The problem is to solve the equation $2x^2 - 10x = -12$ by graphing the related function and finding its zeros. 2. First, rewrite the equation in standard form by moving all terms to one side: $$2x^2 - 10x + 12 = 0$$ 3. The related function to graph is: $$y = 2x^2 - 10x + 12$$ 4. To find the zeros of the function (where $y=0$), we solve the quadratic equation: $$2x^2 - 10x + 12 = 0$$ 5. Divide the entire equation by 2 to simplify: $$\cancel{2}x^2 - \cancel{2}5x + \cancel{2}6 = 0 \Rightarrow x^2 - 5x + 6 = 0$$ 6. Factor the quadratic: $$x^2 - 5x + 6 = (x - 2)(x - 3) = 0$$ 7. Set each factor equal to zero and solve for $x$: $$x - 2 = 0 \Rightarrow x = 2$$ $$x - 3 = 0 \Rightarrow x = 3$$ 8. These values $x=2$ and $x=3$ are the zeros of the function, meaning the points where the graph crosses the x-axis. 9. Graphing $y = 2x^2 - 10x + 12$ will show a parabola opening upwards with zeros at $x=2$ and $x=3$. Final answer: The solutions to the equation are $x=2$ and $x=3$.