3p(p+7)(5p-3)=0

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Solution for 3p(p+7)(5p-3)=0 equation: 


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

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

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

Multiply (7 + p) * (-3 + 5p)
3p(7(-3 + 5p) + p(-3 + 5p)) = 0
3p((-3 * 7 + 5p * 7) + p(-3 + 5p)) = 0
3p((-21 + 35p) + p(-3 + 5p)) = 0
3p(-21 + 35p + (-3 * p + 5p * p)) = 0
3p(-21 + 35p + (-3p + 5p2)) = 0

Combine like terms: 35p + -3p = 32p
3p(-21 + 32p + 5p2) = 0
(-21 * 3p + 32p * 3p + 5p2 * 3p) = 0
(-63p + 96p2 + 15p3) = 0

Solving
-63p + 96p2 + 15p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p'.
3p(-21 + 32p + 5p2) = 0

Factor a trinomial.
3p((-7 + -1p)(3 + -5p)) = 0

Ignore the factor 3.

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 '(-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

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

Simplifying
3 + -5p = 0

Solving
3 + -5p = 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 + -5p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5p = 0 + -3
-5p = 0 + -3

Combine like terms: 0 + -3 = -3
-5p = -3

Divide each side by '-5'.
p = 0.6

Simplifying
p = 0.6
Solution
p = {0, -7, 0.6}

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