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Simplifying 3a2pq + 3abpq + -90b2pq = 0 Reorder the terms: 3abpq + 3a2pq + -90b2pq = 0 Solving 3abpq + 3a2pq + -90b2pq = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3pq'. 3pq(ab + a2 + -30b2) = 0 Factor a trinomial. 3pq((a + -5b)(a + 6b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'pq' equal to zero and attempt to solve: Simplifying pq = 0 Solving pq = 0 Move all terms containing a to the left, all other terms to the right. Add '-1pq' to each side of the equation. pq + -1pq = 0 + -1pq Remove the zero: 0 = -1pq Simplifying 0 = -1pq The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(a + -5b)' equal to zero and attempt to solve: Simplifying a + -5b = 0 Solving a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 a + 0 = 0 + 5b a = 0 + 5b Remove the zero: a = 5b Simplifying a = 5bSubproblem 3
Set the factor '(a + 6b)' equal to zero and attempt to solve: Simplifying a + 6b = 0 Solving a + 6b = 0 Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. a + 6b + -6b = 0 + -6b Combine like terms: 6b + -6b = 0 a + 0 = 0 + -6b a = 0 + -6b Remove the zero: a = -6b Simplifying a = -6bSolution
a = {5b, -6b}
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