(1+4p)=(4p-1)(p+2)

Solution for (1+4p)=(4p-1)(p+2) equation:

(1+4p)=(4p-1)(p+2)

We move all terms to the left:

(1+4p)-((4p-1)(p+2))=0

We add all the numbers together, and all the variables

(4p+1)-((4p-1)(p+2))=0

We get rid of parentheses

4p-((4p-1)(p+2))+1=0

We multiply parentheses ..

-((+4p^2+8p-1p-2))+4p+1=0


We calculate terms in parentheses: -((+4p^2+8p-1p-2)), so:

(+4p^2+8p-1p-2)

We get rid of parentheses

4p^2+8p-1p-2

We add all the numbers together, and all the variables

4p^2+7p-2

Back to the equation:

-(4p^2+7p-2)


We add all the numbers together, and all the variables

4p-(4p^2+7p-2)+1=0

We get rid of parentheses

-4p^2+4p-7p+2+1=0

We add all the numbers together, and all the variables

-4p^2-3p+3=0

a = -4; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-4)·3
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{57}}{2*-4}=\frac{3-\sqrt{57}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*-4}=\frac{3+\sqrt{57}}{-8}
$