1. $3m+8=15$
This equation is not quadratic because it is a linear equation in terms of $m$. It can be simplified to solve for $m$:
$3m=15-8$
$3m=7$
$m=\frac{7}{3}$
Therefore, the equation is BLUFF (not quadratic).
2. $x^2-5x+10=0$
This equation is quadratic because it contains a quadratic term ($x^2$). It is in the standard form of a quadratic equation ($a{x}^2+bx+c=0$), with $a=1$, $b=-5$, and $c=10$. Therefore, the equation is FACT (quadratic).
3. $12-4x=0$
This equation is linear because it is a linear equation in terms of $x$. It can be simplified to solve for $x$:
$-4x=-12$
$x=\frac{-12}{-4}$
$x=3$
Therefore, the equation is BLUFF (not quadratic).
4. $2t^2-7t=12$
This equation is quadratic because it contains a quadratic term ($t^2$). It is in the standard form of a quadratic equation, with $a=2$, $b=-7$, and $c=-12$. Therefore, the equation is FACT (quadratic).
5. $6-2x+3x^2=0$
This equation is quadratic because it contains a quadratic term ($3x^2$). It is in the standard form of a quadratic equation, with $a=3$, $b=-2$, and $c=6$. Therefore, the equation is FACT (quadratic).
6. $25-r^2=4r-5r^2+10$
This equation is quadratic because it contains a quadratic term ($r^2$). It can be simplified and rearranged to get all terms on one side:
$-4r+4r^2-r^2-25+10=0$
$3r^2-4r-15=0$
Therefore, the equation is FACT (quadratic).
7. $3x(x-2)=-7$
This equation is quadratic because it contains a quadratic term ($x^2$) when the expression is expanded. Expanding the equation gives:
$3x^2-6x=-7$
Therefore, the equation is FACT (quadratic).
8. $2h(h-6)=2h+3$
This equation is quadratic because it contains a quadratic term ($h^2$) when the expression is expanded. Expanding the equation gives:
$2h^2-12h=2h+3$
Therefore, the equation is FACT (quadratic).
9. $(x+2{)}^2=0$
This equation is quadratic because it contains a quadratic term ($x^2$) when the expression is expanded. Expanding the equation gives:
$x^2+4x+4=0$
Therefore, the equation is FACT (quadratic).
10. $(w-8)(w+5)=14+w^2$
This equation is not quadratic because when expanded, the quadratic terms cancel out:
$w^2-3w-40=14+w^2$
$-3w-40=14$
$-3w=54$
$w=\frac{54}{-3}$
$w=-18$
Therefore, the equation is BLUFF (not quadratic).