p-1=2p^2-3p+5

Solution for p-1=2p^2-3p+5 equation:

Simplifying
p + -1 = 2p2 + -3p + 5

Reorder the terms:
-1 + p = 2p2 + -3p + 5

Reorder the terms:
-1 + p = 5 + -3p + 2p2

Solving
-1 + p = 5 + -3p + 2p2

Solving for variable 'p'.

Reorder the terms:
-1 + -5 + p + 3p + -2p2 = 5 + -3p + 2p2 + -5 + 3p + -2p2

Combine like terms: -1 + -5 = -6
-6 + p + 3p + -2p2 = 5 + -3p + 2p2 + -5 + 3p + -2p2

Combine like terms: p + 3p = 4p
-6 + 4p + -2p2 = 5 + -3p + 2p2 + -5 + 3p + -2p2

Reorder the terms:
-6 + 4p + -2p2 = 5 + -5 + -3p + 3p + 2p2 + -2p2

Combine like terms: 5 + -5 = 0
-6 + 4p + -2p2 = 0 + -3p + 3p + 2p2 + -2p2
-6 + 4p + -2p2 = -3p + 3p + 2p2 + -2p2

Combine like terms: -3p + 3p = 0
-6 + 4p + -2p2 = 0 + 2p2 + -2p2
-6 + 4p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-6 + 4p + -2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2p + -1p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2p + -1p2)' equal to zero and attempt to solve:

Simplifying
-3 + 2p + -1p2 = 0

Solving
-3 + 2p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -2p + p2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2p + -3 + p2 = 0 + -3

Reorder the terms:
3 + -3 + -2p + p2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2p + p2 = 0 + -3
-2p + p2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2p + p2 = -3

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = -3 + 1

Reorder the terms:
1 + -2p + p2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + -2p + p2 = -2

Factor a perfect square on the left side:
(p + -1)(p + -1) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.