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Simplifying 12a2z2 + -42az2 + -90z2 = 0 Reorder the terms: -42az2 + 12a2z2 + -90z2 = 0 Solving -42az2 + 12a2z2 + -90z2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '6z2'. 6z2(-7a + 2a2 + -15) = 0 Factor a trinomial. 6z2((a + -5)(2a + 3)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve: Simplifying z2 = 0 Solving z2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1z2' to each side of the equation. z2 + -1z2 = 0 + -1z2 Remove the zero: 0 = -1z2 Simplifying 0 = -1z2 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 + -5)' equal to zero and attempt to solve: Simplifying a + -5 = 0 Reorder the terms: -5 + a = 0 Solving -5 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + a = 0 + 5 a = 0 + 5 Combine like terms: 0 + 5 = 5 a = 5 Simplifying a = 5Subproblem 3
Set the factor '(2a + 3)' equal to zero and attempt to solve: Simplifying 2a + 3 = 0 Reorder the terms: 3 + 2a = 0 Solving 3 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2a = 0 + -3 2a = 0 + -3 Combine like terms: 0 + -3 = -3 2a = -3 Divide each side by '2'. a = -1.5 Simplifying a = -1.5Solution
a = {5, -1.5}
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