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Simplifying 5a(-7b + -7a + -7) + 3a(8b + 10a + -8) = 0 Reorder the terms: 5a(-7 + -7a + -7b) + 3a(8b + 10a + -8) = 0 (-7 * 5a + -7a * 5a + -7b * 5a) + 3a(8b + 10a + -8) = 0 Reorder the terms: (-35a + -35ab + -35a2) + 3a(8b + 10a + -8) = 0 (-35a + -35ab + -35a2) + 3a(8b + 10a + -8) = 0 Reorder the terms: -35a + -35ab + -35a2 + 3a(-8 + 10a + 8b) = 0 -35a + -35ab + -35a2 + (-8 * 3a + 10a * 3a + 8b * 3a) = 0 Reorder the terms: -35a + -35ab + -35a2 + (-24a + 24ab + 30a2) = 0 -35a + -35ab + -35a2 + (-24a + 24ab + 30a2) = 0 Reorder the terms: -35a + -24a + -35ab + 24ab + -35a2 + 30a2 = 0 Combine like terms: -35a + -24a = -59a -59a + -35ab + 24ab + -35a2 + 30a2 = 0 Combine like terms: -35ab + 24ab = -11ab -59a + -11ab + -35a2 + 30a2 = 0 Combine like terms: -35a2 + 30a2 = -5a2 -59a + -11ab + -5a2 = 0 Solving -59a + -11ab + -5a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '-1a'. -1a(59 + 11b + 5a) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(59 + 11b + 5a)' equal to zero and attempt to solve: Simplifying 59 + 11b + 5a = 0 Reorder the terms: 59 + 5a + 11b = 0 Solving 59 + 5a + 11b = 0 Move all terms containing a to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + 5a + -59 + 11b = 0 + -59 Reorder the terms: 59 + -59 + 5a + 11b = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 5a + 11b = 0 + -59 5a + 11b = 0 + -59 Combine like terms: 0 + -59 = -59 5a + 11b = -59 Add '-11b' to each side of the equation. 5a + 11b + -11b = -59 + -11b Combine like terms: 11b + -11b = 0 5a + 0 = -59 + -11b 5a = -59 + -11b Divide each side by '5'. a = -11.8 + -2.2b Simplifying a = -11.8 + -2.2bSolution
a = {0, -11.8 + -2.2b}
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