Given the functions f(x)=x^2-x and g(x)=x^2-3x-12 solve the equation f(x)=6 b solve the equation f(x)=g(x)

To solve the equation $f(x)=6$, we need to find the value of $x$ that makes $f(x)$ equal to 6.<br /><br />Given the function $f(x)=x^{2}-x$, we can set it equal to 6 and solve for $x$:<br /><br />$x^{2}-x=6$<br /><br />Rearranging the equation, we get:<br /><br />$x^{2}-x-6=0$<br /><br />Factoring the quadratic equation, we have:<br /><br />$(x-3)(x+2)=0$<br /><br />Setting each factor equal to zero, we get:<br /><br />$x-3=0$ or $x+2=0$<br /><br />Solving for $x$, we find:<br /><br />$x=3$ or $x=-2$<br /><br />Therefore, the solutions to the equation $f(x)=6$ are $x=3$ and $x=-2$.<br /><br />To solve the equation $f(x)=g(x)$, we need to find the value of $x$ that makes $f(x)$ equal to $g(x)$.<br /><br />Given the functions $f(x)=x^{2}-x$ and $g(x)=x^{2}-3x-12$, we can set them equal to each other and solve for $x$:<br /><br />$x^{2}-x=x^{2}-3x-12$<br /><br />Simplifying the equation, we get:<br /><br />$2x=-12$<br /><br />Dividing both sides by 2, we find:<br /><br />$x=-6$<br /><br />Therefore, the solution to the equation $f(x)=g(x)$ is $x=-6$.