(p-4)(p-1)=18

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Solution for (p-4)(p-1)=18 equation: 


Simplifying
(p + -4)(p + -1) = 18

Reorder the terms:
(-4 + p)(p + -1) = 18

Reorder the terms:
(-4 + p)(-1 + p) = 18

Multiply (-4 + p) * (-1 + p)
(-4(-1 + p) + p(-1 + p)) = 18
((-1 * -4 + p * -4) + p(-1 + p)) = 18
((4 + -4p) + p(-1 + p)) = 18
(4 + -4p + (-1 * p + p * p)) = 18
(4 + -4p + (-1p + p2)) = 18

Combine like terms: -4p + -1p = -5p
(4 + -5p + p2) = 18

Solving
4 + -5p + p2 = 18

Solving for variable 'p'.

Reorder the terms:
4 + -18 + -5p + p2 = 18 + -18

Combine like terms: 4 + -18 = -14
-14 + -5p + p2 = 18 + -18

Combine like terms: 18 + -18 = 0
-14 + -5p + p2 = 0

Factor a trinomial.
(-2 + -1p)(7 + -1p) = 0


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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2

Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve:

Simplifying
7 + -1p = 0

Solving
7 + -1p = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1p = 0 + -7

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

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

Divide each side by '-1'.
p = 7

Simplifying
p = 7
Solution
p = {-2, 7}

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