10p^4+31p^3q+3p^2q^2=

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Solution for 10p^4+31p^3q+3p^2q^2= equation:


Simplifying
10p4 + 31p3q + 3p2q2 = 0

Reorder the terms:
3p2q2 + 31p3q + 10p4 = 0

Solving
3p2q2 + 31p3q + 10p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(3q2 + 31pq + 10p2) = 0

Factor a trinomial.
p2((3q + p)(q + 10p)) = 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 '(3q + p)' equal to zero and attempt to solve: Simplifying 3q + p = 0 Reorder the terms: p + 3q = 0 Solving p + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. p + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 p + 0 = 0 + -3q p = 0 + -3q Remove the zero: p = -3q Simplifying p = -3q

Subproblem 3

Set the factor '(q + 10p)' equal to zero and attempt to solve: Simplifying q + 10p = 0 Reorder the terms: 10p + q = 0 Solving 10p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 10p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 10p + 0 = 0 + -1q 10p = 0 + -1q Remove the zero: 10p = -1q Divide each side by '10'. p = -0.1q Simplifying p = -0.1q

Solution

p = {0, -3q, -0.1q}

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