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Simplifying 3x(4a + -5b) + -6y(4a + -5b) = 0 (4a * 3x + -5b * 3x) + -6y(4a + -5b) = 0 (12ax + -15bx) + -6y(4a + -5b) = 0 12ax + -15bx + (4a * -6y + -5b * -6y) = 0 12ax + -15bx + (-24ay + 30by) = 0 Reorder the terms: 12ax + -24ay + -15bx + 30by = 0 Solving 12ax + -24ay + -15bx + 30by = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15bx' to each side of the equation. 12ax + -24ay + -15bx + 15bx + 30by = 0 + 15bx Combine like terms: -15bx + 15bx = 0 12ax + -24ay + 0 + 30by = 0 + 15bx 12ax + -24ay + 30by = 0 + 15bx Remove the zero: 12ax + -24ay + 30by = 15bx Add '-30by' to each side of the equation. 12ax + -24ay + 30by + -30by = 15bx + -30by Combine like terms: 30by + -30by = 0 12ax + -24ay + 0 = 15bx + -30by 12ax + -24ay = 15bx + -30by Reorder the terms: 12ax + -24ay + -15bx + 30by = 15bx + -15bx + -30by + 30by Combine like terms: 15bx + -15bx = 0 12ax + -24ay + -15bx + 30by = 0 + -30by + 30by 12ax + -24ay + -15bx + 30by = -30by + 30by Combine like terms: -30by + 30by = 0 12ax + -24ay + -15bx + 30by = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4ax + -8ay + -5bx + 10by) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4ax + -8ay + -5bx + 10by)' equal to zero and attempt to solve: Simplifying 4ax + -8ay + -5bx + 10by = 0 Solving 4ax + -8ay + -5bx + 10by = 0 Move all terms containing a to the left, all other terms to the right. Add '5bx' to each side of the equation. 4ax + -8ay + -5bx + 5bx + 10by = 0 + 5bx Combine like terms: -5bx + 5bx = 0 4ax + -8ay + 0 + 10by = 0 + 5bx 4ax + -8ay + 10by = 0 + 5bx Remove the zero: 4ax + -8ay + 10by = 5bx Add '-10by' to each side of the equation. 4ax + -8ay + 10by + -10by = 5bx + -10by Combine like terms: 10by + -10by = 0 4ax + -8ay + 0 = 5bx + -10by 4ax + -8ay = 5bx + -10by 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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