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Simplifying 10a2b + 45ab + -175b = 0 Reorder the terms: 45ab + 10a2b + -175b = 0 Solving 45ab + 10a2b + -175b = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5b'. 5b(9a + 2a2 + -35) = 0 Factor a trinomial. 5b((2a + -5)(a + 7)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. b + -1b = 0 + -1b Remove the zero: 0 = -1b Simplifying 0 = -1b 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 '(2a + -5)' equal to zero and attempt to solve: Simplifying 2a + -5 = 0 Reorder the terms: -5 + 2a = 0 Solving -5 + 2a = 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 + 2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2a = 0 + 5 2a = 0 + 5 Combine like terms: 0 + 5 = 5 2a = 5 Divide each side by '2'. a = 2.5 Simplifying a = 2.5Subproblem 3
Set the factor '(a + 7)' equal to zero and attempt to solve: Simplifying a + 7 = 0 Reorder the terms: 7 + a = 0 Solving 7 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + a = 0 + -7 a = 0 + -7 Combine like terms: 0 + -7 = -7 a = -7 Simplifying a = -7Solution
a = {2.5, -7}
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