3p-5=(p-1)(p-2)

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Solution for 3p-5=(p-1)(p-2) equation:


Simplifying
3p + -5 = (p + -1)(p + -2)

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

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

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

Multiply (-1 + p) * (-2 + p)
-5 + 3p = (-1(-2 + p) + p(-2 + p))
-5 + 3p = ((-2 * -1 + p * -1) + p(-2 + p))
-5 + 3p = ((2 + -1p) + p(-2 + p))
-5 + 3p = (2 + -1p + (-2 * p + p * p))
-5 + 3p = (2 + -1p + (-2p + p2))

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

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

Solving for variable 'p'.

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

Combine like terms: -5 + -2 = -7
-7 + 3p + 3p + -1p2 = 2 + -3p + p2 + -2 + 3p + -1p2

Combine like terms: 3p + 3p = 6p
-7 + 6p + -1p2 = 2 + -3p + p2 + -2 + 3p + -1p2

Reorder the terms:
-7 + 6p + -1p2 = 2 + -2 + -3p + 3p + p2 + -1p2

Combine like terms: 2 + -2 = 0
-7 + 6p + -1p2 = 0 + -3p + 3p + p2 + -1p2
-7 + 6p + -1p2 = -3p + 3p + p2 + -1p2

Combine like terms: -3p + 3p = 0
-7 + 6p + -1p2 = 0 + p2 + -1p2
-7 + 6p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
-7 + 6p + -1p2 = 0

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

Divide each side by '-1'.
7 + -6p + p2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6p + -7 + p2 = 0 + -7

Reorder the terms:
7 + -7 + -6p + p2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6p + p2 = 0 + -7
-6p + p2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6p + p2 = -7

The p term is -6p.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6p + 9 + p2 = -7 + 9

Reorder the terms:
9 + -6p + p2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6p + p2 = 2

Factor a perfect square on the left side:
(p + -3)(p + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(p + -3) equal to 1.414213562 and -1.414213562.

Subproblem 1

p + -3 = 1.414213562 Simplifying p + -3 = 1.414213562 Reorder the terms: -3 + p = 1.414213562 Solving -3 + p = 1.414213562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + p = 1.414213562 + 3 p = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 p = 4.414213562 Simplifying p = 4.414213562

Subproblem 2

p + -3 = -1.414213562 Simplifying p + -3 = -1.414213562 Reorder the terms: -3 + p = -1.414213562 Solving -3 + p = -1.414213562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + p = -1.414213562 + 3 p = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 p = 1.585786438 Simplifying p = 1.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.414213562, 1.585786438}

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