Subtract 3p2 from both sides of the equation.
Move 84 to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
Let u=p. Substitute u for all occurrences of p.
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=-3⋅-84=252 and whose sum is b=67.
Factor 67 out of 67u.
Rewrite 67 as 4 plus 63
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, -3u+4.
Replace all occurrences of u with p.
Replace the left side with the factored expression.
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
Subtract 4 from both sides of the equation.
Divide each term by -3 and simplify.
Divide each term in -3p=-4 by -3.
Cancel the common factor of -3.
Cancel the common factor.
Divide p by 1.
Dividing two negative values results in a positive value.
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
Add 21 to both sides of the equation.
The final solution is all the values that make (-3p+4)(p-21)=0 true.
The result can be shown in multiple forms.
Mixed Number Form:
Solve for p 67p=3p^2+84