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Simplifying (4u + 3as2)(2u + -2as2) = 0 Reorder the terms: (3as2 + 4u)(2u + -2as2) = 0 Reorder the terms: (3as2 + 4u)(-2as2 + 2u) = 0 Multiply (3as2 + 4u) * (-2as2 + 2u) (3as2 * (-2as2 + 2u) + 4u * (-2as2 + 2u)) = 0 ((-2as2 * 3as2 + 2u * 3as2) + 4u * (-2as2 + 2u)) = 0 Reorder the terms: ((6as2u + -6a2s4) + 4u * (-2as2 + 2u)) = 0 ((6as2u + -6a2s4) + 4u * (-2as2 + 2u)) = 0 (6as2u + -6a2s4 + (-2as2 * 4u + 2u * 4u)) = 0 (6as2u + -6a2s4 + (-8as2u + 8u2)) = 0 Reorder the terms: (6as2u + -8as2u + -6a2s4 + 8u2) = 0 Combine like terms: 6as2u + -8as2u = -2as2u (-2as2u + -6a2s4 + 8u2) = 0 Solving -2as2u + -6a2s4 + 8u2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1as2u + -3a2s4 + 4u2) = 0 Factor a trinomial. 2((-3as2 + -4u)(as2 + -1u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3as2 + -4u)' equal to zero and attempt to solve: Simplifying -3as2 + -4u = 0 Solving -3as2 + -4u = 0 Move all terms containing a to the left, all other terms to the right. Add '4u' to each side of the equation. -3as2 + -4u + 4u = 0 + 4u Combine like terms: -4u + 4u = 0 -3as2 + 0 = 0 + 4u -3as2 = 0 + 4u Remove the zero: -3as2 = 4u Divide each side by '-3s2'. a = -1.333333333s-2u Simplifying a = -1.333333333s-2uSubproblem 2
Set the factor '(as2 + -1u)' equal to zero and attempt to solve: Simplifying as2 + -1u = 0 Solving as2 + -1u = 0 Move all terms containing a to the left, all other terms to the right. Add 'u' to each side of the equation. as2 + -1u + u = 0 + u Combine like terms: -1u + u = 0 as2 + 0 = 0 + u as2 = 0 + u Remove the zero: as2 = u Divide each side by 's2'. a = s-2u Simplifying a = s-2uSolution
a = {-1.333333333s-2u, s-2u}
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