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Simplifying (6 + 2s)(8 + 7r) = 0 Multiply (6 + 2s) * (8 + 7r) (6(8 + 7r) + 2s * (8 + 7r)) = 0 ((8 * 6 + 7r * 6) + 2s * (8 + 7r)) = 0 ((48 + 42r) + 2s * (8 + 7r)) = 0 (48 + 42r + (8 * 2s + 7r * 2s)) = 0 Reorder the terms: (48 + 42r + (14rs + 16s)) = 0 (48 + 42r + (14rs + 16s)) = 0 (48 + 42r + 14rs + 16s) = 0 Solving 48 + 42r + 14rs + 16s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + 42r + 14rs + -48 + 16s = 0 + -48 Reorder the terms: 48 + -48 + 42r + 14rs + 16s = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 42r + 14rs + 16s = 0 + -48 42r + 14rs + 16s = 0 + -48 Combine like terms: 0 + -48 = -48 42r + 14rs + 16s = -48 Add '-16s' to each side of the equation. 42r + 14rs + 16s + -16s = -48 + -16s Combine like terms: 16s + -16s = 0 42r + 14rs + 0 = -48 + -16s 42r + 14rs = -48 + -16s Reorder the terms: 48 + 42r + 14rs + 16s = -48 + -16s + 48 + 16s Reorder the terms: 48 + 42r + 14rs + 16s = -48 + 48 + -16s + 16s Combine like terms: -48 + 48 = 0 48 + 42r + 14rs + 16s = 0 + -16s + 16s 48 + 42r + 14rs + 16s = -16s + 16s Combine like terms: -16s + 16s = 0 48 + 42r + 14rs + 16s = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 21r + 7rs + 8s) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + 21r + 7rs + 8s)' equal to zero and attempt to solve: Simplifying 24 + 21r + 7rs + 8s = 0 Solving 24 + 21r + 7rs + 8s = 0 Move all terms containing r to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + 21r + 7rs + -24 + 8s = 0 + -24 Reorder the terms: 24 + -24 + 21r + 7rs + 8s = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 21r + 7rs + 8s = 0 + -24 21r + 7rs + 8s = 0 + -24 Combine like terms: 0 + -24 = -24 21r + 7rs + 8s = -24 Add '-8s' to each side of the equation. 21r + 7rs + 8s + -8s = -24 + -8s Combine like terms: 8s + -8s = 0 21r + 7rs + 0 = -24 + -8s 21r + 7rs = -24 + -8s 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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