(p+5)(p-4)=90

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Solution for (p+5)(p-4)=90 equation: 


Simplifying
(p + 5)(p + -4) = 90

Reorder the terms:
(5 + p)(p + -4) = 90

Reorder the terms:
(5 + p)(-4 + p) = 90

Multiply (5 + p) * (-4 + p)
(5(-4 + p) + p(-4 + p)) = 90
((-4 * 5 + p * 5) + p(-4 + p)) = 90
((-20 + 5p) + p(-4 + p)) = 90
(-20 + 5p + (-4 * p + p * p)) = 90
(-20 + 5p + (-4p + p2)) = 90

Combine like terms: 5p + -4p = 1p
(-20 + 1p + p2) = 90

Solving
-20 + 1p + p2 = 90

Solving for variable 'p'.

Reorder the terms:
-20 + -90 + 1p + p2 = 90 + -90

Combine like terms: -20 + -90 = -110
-110 + 1p + p2 = 90 + -90

Combine like terms: 90 + -90 = 0
-110 + 1p + p2 = 0

Factor a trinomial.
(-11 + -1p)(10 + -1p) = 0


Subproblem 1
Set the factor '(-11 + -1p)' equal to zero and attempt to solve:

Simplifying
-11 + -1p = 0

Solving
-11 + -1p = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1p = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1p = 0 + 11
-1p = 0 + 11

Combine like terms: 0 + 11 = 11
-1p = 11

Divide each side by '-1'.
p = -11

Simplifying
p = -11

Subproblem 2
Set the factor '(10 + -1p)' equal to zero and attempt to solve:

Simplifying
10 + -1p = 0

Solving
10 + -1p = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1p = 0 + -10
-1p = 0 + -10

Combine like terms: 0 + -10 = -10
-1p = -10

Divide each side by '-1'.
p = 10

Simplifying
p = 10
Solution
p = {-11, 10}

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