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Simplifying 6b4 + -39b2 + -135 = 0 Reorder the terms: -135 + -39b2 + 6b4 = 0 Solving -135 + -39b2 + 6b4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-45 + -13b2 + 2b4) = 0 Factor a trinomial. 3((-5 + -2b2)(9 + -1b2)) = 0 Factor a difference between two squares. 3((-5 + -2b2)((3 + b)(3 + -1b))) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -2b2)' equal to zero and attempt to solve: Simplifying -5 + -2b2 = 0 Solving -5 + -2b2 = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2b2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2b2 = 0 + 5 -2b2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2b2 = 5 Divide each side by '-2'. b2 = -2.5 Simplifying b2 = -2.5 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 '(3 + b)' equal to zero and attempt to solve: Simplifying 3 + b = 0 Solving 3 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b = 0 + -3 b = 0 + -3 Combine like terms: 0 + -3 = -3 b = -3 Simplifying b = -3Subproblem 3
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-3, 3}
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