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Simplifying a(-2b + 2c) + -3a(b + 5c) = 0 (-2b * a + 2c * a) + -3a(b + 5c) = 0 (-2ab + 2ac) + -3a(b + 5c) = 0 -2ab + 2ac + (b * -3a + 5c * -3a) = 0 -2ab + 2ac + (-3ab + -15ac) = 0 Reorder the terms: -2ab + -3ab + 2ac + -15ac = 0 Combine like terms: -2ab + -3ab = -5ab -5ab + 2ac + -15ac = 0 Combine like terms: 2ac + -15ac = -13ac -5ab + -13ac = 0 Solving -5ab + -13ac = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '-1a'. -1a(5b + 13c) = 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 '(5b + 13c)' equal to zero and attempt to solve: Simplifying 5b + 13c = 0 Solving 5b + 13c = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 5b + -5b + 13c = 0 + -5b Combine like terms: 5b + -5b = 0 0 + 13c = 0 + -5b 13c = 0 + -5b Remove the zero: 13c = -5b Add '-13c' to each side of the equation. 13c + -13c = -5b + -13c Combine like terms: 13c + -13c = 0 0 = -5b + -13c Simplifying 0 = -5b + -13c The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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