(p^2-3p)(p^2-3p)=0

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Solution for (p^2-3p)(p^2-3p)=0 equation:


Simplifying
(p2 + -3p)(p2 + -3p) = 0

Reorder the terms:
(-3p + p2)(p2 + -3p) = 0

Reorder the terms:
(-3p + p2)(-3p + p2) = 0

Multiply (-3p + p2) * (-3p + p2)
(-3p * (-3p + p2) + p2(-3p + p2)) = 0
((-3p * -3p + p2 * -3p) + p2(-3p + p2)) = 0
((9p2 + -3p3) + p2(-3p + p2)) = 0
(9p2 + -3p3 + (-3p * p2 + p2 * p2)) = 0
(9p2 + -3p3 + (-3p3 + p4)) = 0

Combine like terms: -3p3 + -3p3 = -6p3
(9p2 + -6p3 + p4) = 0

Solving
9p2 + -6p3 + p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(9 + -6p + p2) = 0

Factor a trinomial.
p2((3 + -1p)(3 + -1p)) = 0

Subproblem 1

Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}

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

Subproblem 3

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 = {0, 3, 3}

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