Answer:
[tex]m^2-m=0[/tex]
or [tex]m^2=m[/tex]
Step-by-step explanation:
you have a definition for the variable m:
[tex]m=2x+3[/tex]
and then you are asked to find the equivalent equation to:
[tex](2x+3)^2-14x-21=-6(2x+3)[/tex]
in terms of m, what we need to do is substitute all the [tex]2x+3[/tex] we find in the expression, for an m (because of the definition [tex]m=2x+3[/tex]), this way we get the following:
[tex]m^2-14x-21=-6m[/tex]
we still have to write [tex]-14x-21[/tex] in terms of m for that we factor a -7, and we get:
[tex]-14x-21=-7(2x+3)[/tex]
we have found an equivalent to [tex]-14x-21[/tex] which contains [tex]2x+3[/tex] and since we know that [tex]m=2x+3[/tex]:
[tex]-14x-21=-7m[/tex]
and we substitute this into the equation
[tex]m^2-14x-21=-6m[/tex]
[tex]m^2-7m=-6m[/tex]
this equation is now what we anted, the original expression in terms of m. you can represent the result like this:
[tex]m^2-7m+6m=0\\m^2-m=0[/tex]
or what is the same: [tex]m^2=m[/tex]
