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Simplifying 8pq2 + 8pq + 2p = 0 Reorder the terms: 2p + 8pq + 8pq2 = 0 Solving 2p + 8pq + 8pq2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2p'. 2p(1 + 4q + 4q2) = 0 Factor a trinomial. 2p((1 + 2q)(1 + 2q)) = 0 Ignore the factor 2.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 = 0Subproblem 2
Set the factor '(1 + 2q)' equal to zero and attempt to solve: Simplifying 1 + 2q = 0 Solving 1 + 2q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2q = 0 + -1 2q = 0 + -1 Combine like terms: 0 + -1 = -1 2q = -1 Add '-2q' to each side of the equation. 2q + -2q = -1 + -2q Combine like terms: 2q + -2q = 0 0 = -1 + -2q Simplifying 0 = -1 + -2q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + 2q)' equal to zero and attempt to solve: Simplifying 1 + 2q = 0 Solving 1 + 2q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2q = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2q = 0 + -1 2q = 0 + -1 Combine like terms: 0 + -1 = -1 2q = -1 Add '-2q' to each side of the equation. 2q + -2q = -1 + -2q Combine like terms: 2q + -2q = 0 0 = -1 + -2q Simplifying 0 = -1 + -2q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
p = {0}
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