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

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


Simplifying
(p + 5) * x(p + -2) = 0

Reorder the terms:
(5 + p) * x(p + -2) = 0

Reorder the terms:
(5 + p) * x(-2 + p) = 0

Reorder the terms for easier multiplication:
x(5 + p)(-2 + p) = 0

Multiply (5 + p) * (-2 + p)
x(5(-2 + p) + p(-2 + p)) = 0
x((-2 * 5 + p * 5) + p(-2 + p)) = 0
x((-10 + 5p) + p(-2 + p)) = 0
x(-10 + 5p + (-2 * p + p * p)) = 0
x(-10 + 5p + (-2p + p2)) = 0

Combine like terms: 5p + -2p = 3p
x(-10 + 3p + p2) = 0
(-10 * x + 3p * x + p2 * x) = 0

Reorder the terms:
(3px + p2x + -10x) = 0
(3px + p2x + -10x) = 0

Solving
3px + p2x + -10x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3p + p2 + -10) = 0

Factor a trinomial.
x((p + -2)(p + 5)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
p + -2 = 0

Reorder the terms:
-2 + p = 0

Solving
-2 + p = 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 + p = 0 + 2

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

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

Simplifying
p = 2

Subproblem 3
Set the factor '(p + 5)' equal to zero and attempt to solve:

Simplifying
p + 5 = 0

Reorder the terms:
5 + p = 0

Solving
5 + p = 0

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

Add '-5' to each side of the equation.
5 + -5 + p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + p = 0 + -5
p = 0 + -5

Combine like terms: 0 + -5 = -5
p = -5

Simplifying
p = -5
Solution
p = {2, -5}

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