4(p-3)(p+8)=0

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Solution for 4(p-3)(p+8)=0 equation: 


Simplifying
4(p + -3)(p + 8) = 0

Reorder the terms:
4(-3 + p)(p + 8) = 0

Reorder the terms:
4(-3 + p)(8 + p) = 0

Multiply (-3 + p) * (8 + p)
4(-3(8 + p) + p(8 + p)) = 0
4((8 * -3 + p * -3) + p(8 + p)) = 0
4((-24 + -3p) + p(8 + p)) = 0
4(-24 + -3p + (8 * p + p * p)) = 0
4(-24 + -3p + (8p + p2)) = 0

Combine like terms: -3p + 8p = 5p
4(-24 + 5p + p2) = 0
(-24 * 4 + 5p * 4 + p2 * 4) = 0
(-96 + 20p + 4p2) = 0

Solving
-96 + 20p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 5p + p2) = 0

Factor a trinomial.
4((-8 + -1p)(3 + -1p)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + -1p)' equal to zero and attempt to solve:

Simplifying
-8 + -1p = 0

Solving
-8 + -1p = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1p = 0 + 8
-1p = 0 + 8

Combine like terms: 0 + 8 = 8
-1p = 8

Divide each side by '-1'.
p = -8

Simplifying
p = -8

Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-8, 3}

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