3p(p+5)4(p-7)=

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Solution for 3p(p+5)4(p-7)= equation: 


Simplifying
3p(p + 5) * 4(p + -7) = 0

Reorder the terms:
3p(5 + p) * 4(p + -7) = 0

Reorder the terms:
3p(5 + p) * 4(-7 + p) = 0

Reorder the terms for easier multiplication:
3 * 4p(5 + p)(-7 + p) = 0

Multiply 3 * 4
12p(5 + p)(-7 + p) = 0

Multiply (5 + p) * (-7 + p)
12p(5(-7 + p) + p(-7 + p)) = 0
12p((-7 * 5 + p * 5) + p(-7 + p)) = 0
12p((-35 + 5p) + p(-7 + p)) = 0
12p(-35 + 5p + (-7 * p + p * p)) = 0
12p(-35 + 5p + (-7p + p2)) = 0

Combine like terms: 5p + -7p = -2p
12p(-35 + -2p + p2) = 0
(-35 * 12p + -2p * 12p + p2 * 12p) = 0
(-420p + -24p2 + 12p3) = 0

Solving
-420p + -24p2 + 12p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '12p'.
12p(-35 + -2p + p2) = 0

Factor a trinomial.
12p((-5 + -1p)(7 + -1p)) = 0

Ignore the factor 12.

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0

Subproblem 2
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 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 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5

Subproblem 3
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 = {0, -5, 7}

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