(2p-5)(p-4)=p+8

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Solution for (2p-5)(p-4)=p+8 equation: 


Simplifying
(2p + -5)(p + -4) = p + 8

Reorder the terms:
(-5 + 2p)(p + -4) = p + 8

Reorder the terms:
(-5 + 2p)(-4 + p) = p + 8

Multiply (-5 + 2p) * (-4 + p)
(-5(-4 + p) + 2p * (-4 + p)) = p + 8
((-4 * -5 + p * -5) + 2p * (-4 + p)) = p + 8
((20 + -5p) + 2p * (-4 + p)) = p + 8
(20 + -5p + (-4 * 2p + p * 2p)) = p + 8
(20 + -5p + (-8p + 2p2)) = p + 8

Combine like terms: -5p + -8p = -13p
(20 + -13p + 2p2) = p + 8

Reorder the terms:
20 + -13p + 2p2 = 8 + p

Solving
20 + -13p + 2p2 = 8 + p

Solving for variable 'p'.

Reorder the terms:
20 + -8 + -13p + -1p + 2p2 = 8 + p + -8 + -1p

Combine like terms: 20 + -8 = 12
12 + -13p + -1p + 2p2 = 8 + p + -8 + -1p

Combine like terms: -13p + -1p = -14p
12 + -14p + 2p2 = 8 + p + -8 + -1p

Reorder the terms:
12 + -14p + 2p2 = 8 + -8 + p + -1p

Combine like terms: 8 + -8 = 0
12 + -14p + 2p2 = 0 + p + -1p
12 + -14p + 2p2 = p + -1p

Combine like terms: p + -1p = 0
12 + -14p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -7p + p2) = 0

Factor a trinomial.
2((1 + -1p)(6 + -1p)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1p = 0 + -1
-1p = 0 + -1

Combine like terms: 0 + -1 = -1
-1p = -1

Divide each side by '-1'.
p = 1

Simplifying
p = 1

Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

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

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

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {1, 6}

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