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Simplifying (5m + 2n)(6t + -2s) = 0 Reorder the terms: (5m + 2n)(-2s + 6t) = 0 Multiply (5m + 2n) * (-2s + 6t) (5m * (-2s + 6t) + 2n * (-2s + 6t)) = 0 ((-2s * 5m + 6t * 5m) + 2n * (-2s + 6t)) = 0 ((-10ms + 30mt) + 2n * (-2s + 6t)) = 0 (-10ms + 30mt + (-2s * 2n + 6t * 2n)) = 0 (-10ms + 30mt + (-4ns + 12nt)) = 0 (-10ms + 30mt + -4ns + 12nt) = 0 Solving -10ms + 30mt + -4ns + 12nt = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4ns' to each side of the equation. -10ms + 30mt + -4ns + 4ns + 12nt = 0 + 4ns Combine like terms: -4ns + 4ns = 0 -10ms + 30mt + 0 + 12nt = 0 + 4ns -10ms + 30mt + 12nt = 0 + 4ns Remove the zero: -10ms + 30mt + 12nt = 4ns Add '-12nt' to each side of the equation. -10ms + 30mt + 12nt + -12nt = 4ns + -12nt Combine like terms: 12nt + -12nt = 0 -10ms + 30mt + 0 = 4ns + -12nt -10ms + 30mt = 4ns + -12nt Reorder the terms: -10ms + 30mt + -4ns + 12nt = 4ns + -4ns + -12nt + 12nt Combine like terms: 4ns + -4ns = 0 -10ms + 30mt + -4ns + 12nt = 0 + -12nt + 12nt -10ms + 30mt + -4ns + 12nt = -12nt + 12nt Combine like terms: -12nt + 12nt = 0 -10ms + 30mt + -4ns + 12nt = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5ms + 15mt + -2ns + 6nt) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5ms + 15mt + -2ns + 6nt)' equal to zero and attempt to solve: Simplifying -5ms + 15mt + -2ns + 6nt = 0 Solving -5ms + 15mt + -2ns + 6nt = 0 Move all terms containing m to the left, all other terms to the right. Add '2ns' to each side of the equation. -5ms + 15mt + -2ns + 2ns + 6nt = 0 + 2ns Combine like terms: -2ns + 2ns = 0 -5ms + 15mt + 0 + 6nt = 0 + 2ns -5ms + 15mt + 6nt = 0 + 2ns Remove the zero: -5ms + 15mt + 6nt = 2ns Add '-6nt' to each side of the equation. -5ms + 15mt + 6nt + -6nt = 2ns + -6nt Combine like terms: 6nt + -6nt = 0 -5ms + 15mt + 0 = 2ns + -6nt -5ms + 15mt = 2ns + -6nt 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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