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

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


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

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

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

Multiply (3 + p) * (-5 + p)
(3(-5 + p) + p(-5 + p)) = 2p + 3
((-5 * 3 + p * 3) + p(-5 + p)) = 2p + 3
((-15 + 3p) + p(-5 + p)) = 2p + 3
(-15 + 3p + (-5 * p + p * p)) = 2p + 3
(-15 + 3p + (-5p + p2)) = 2p + 3

Combine like terms: 3p + -5p = -2p
(-15 + -2p + p2) = 2p + 3

Reorder the terms:
-15 + -2p + p2 = 3 + 2p

Solving
-15 + -2p + p2 = 3 + 2p

Solving for variable 'p'.

Reorder the terms:
-15 + -3 + -2p + -2p + p2 = 3 + 2p + -3 + -2p

Combine like terms: -15 + -3 = -18
-18 + -2p + -2p + p2 = 3 + 2p + -3 + -2p

Combine like terms: -2p + -2p = -4p
-18 + -4p + p2 = 3 + 2p + -3 + -2p

Reorder the terms:
-18 + -4p + p2 = 3 + -3 + 2p + -2p

Combine like terms: 3 + -3 = 0
-18 + -4p + p2 = 0 + 2p + -2p
-18 + -4p + p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-18 + -4p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -4p + 18 + p2 = 0 + 18

Reorder the terms:
-18 + 18 + -4p + p2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -4p + p2 = 0 + 18
-4p + p2 = 0 + 18

Combine like terms: 0 + 18 = 18
-4p + p2 = 18

The p term is -4p.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4p + 4 + p2 = 18 + 4

Reorder the terms:
4 + -4p + p2 = 18 + 4

Combine like terms: 18 + 4 = 22
4 + -4p + p2 = 22

Factor a perfect square on the left side:
(p + -2)(p + -2) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(p + -2) equal to 4.69041576 and -4.69041576.

Subproblem 1

p + -2 = 4.69041576 Simplifying p + -2 = 4.69041576 Reorder the terms: -2 + p = 4.69041576 Solving -2 + p = 4.69041576 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 4.69041576 + 2 Combine like terms: -2 + 2 = 0 0 + p = 4.69041576 + 2 p = 4.69041576 + 2 Combine like terms: 4.69041576 + 2 = 6.69041576 p = 6.69041576 Simplifying p = 6.69041576

Subproblem 2

p + -2 = -4.69041576 Simplifying p + -2 = -4.69041576 Reorder the terms: -2 + p = -4.69041576 Solving -2 + p = -4.69041576 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -4.69041576 + 2 Combine like terms: -2 + 2 = 0 0 + p = -4.69041576 + 2 p = -4.69041576 + 2 Combine like terms: -4.69041576 + 2 = -2.69041576 p = -2.69041576 Simplifying p = -2.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. p = {6.69041576, -2.69041576}

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