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Simplifying 6(10a + 3b) * y = 6(10a + 3b) Reorder the terms for easier multiplication: 6y(10a + 3b) = 6(10a + 3b) (10a * 6y + 3b * 6y) = 6(10a + 3b) (60ay + 18by) = 6(10a + 3b) 60ay + 18by = (10a * 6 + 3b * 6) 60ay + 18by = (60a + 18b) Solving 60ay + 18by = 60a + 18b Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-60a' to each side of the equation. 60ay + -60a + 18by = 60a + -60a + 18b Reorder the terms: -60a + 60ay + 18by = 60a + -60a + 18b Combine like terms: 60a + -60a = 0 -60a + 60ay + 18by = 0 + 18b -60a + 60ay + 18by = 18b Add '-18by' to each side of the equation. -60a + 60ay + 18by + -18by = 18b + -18by Combine like terms: 18by + -18by = 0 -60a + 60ay + 0 = 18b + -18by -60a + 60ay = 18b + -18by Reorder the terms: -60a + 60ay + -18b + 18by = 18b + -18b + -18by + 18by Combine like terms: 18b + -18b = 0 -60a + 60ay + -18b + 18by = 0 + -18by + 18by -60a + 60ay + -18b + 18by = -18by + 18by Combine like terms: -18by + 18by = 0 -60a + 60ay + -18b + 18by = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-10a + 10ay + -3b + 3by) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-10a + 10ay + -3b + 3by)' equal to zero and attempt to solve: Simplifying -10a + 10ay + -3b + 3by = 0 Solving -10a + 10ay + -3b + 3by = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. -10a + 10ay + -3b + 3b + 3by = 0 + 3b Combine like terms: -3b + 3b = 0 -10a + 10ay + 0 + 3by = 0 + 3b -10a + 10ay + 3by = 0 + 3b Remove the zero: -10a + 10ay + 3by = 3b Add '-3by' to each side of the equation. -10a + 10ay + 3by + -3by = 3b + -3by Combine like terms: 3by + -3by = 0 -10a + 10ay + 0 = 3b + -3by -10a + 10ay = 3b + -3by The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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