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Simplifying 4r(s + -3) + -8(s + -3) = 0 Reorder the terms: 4r(-3 + s) + -8(s + -3) = 0 (-3 * 4r + s * 4r) + -8(s + -3) = 0 (-12r + 4rs) + -8(s + -3) = 0 Reorder the terms: -12r + 4rs + -8(-3 + s) = 0 -12r + 4rs + (-3 * -8 + s * -8) = 0 -12r + 4rs + (24 + -8s) = 0 Reorder the terms: 24 + -12r + 4rs + -8s = 0 Solving 24 + -12r + 4rs + -8s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -12r + 4rs + -24 + -8s = 0 + -24 Reorder the terms: 24 + -24 + -12r + 4rs + -8s = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -12r + 4rs + -8s = 0 + -24 -12r + 4rs + -8s = 0 + -24 Combine like terms: 0 + -24 = -24 -12r + 4rs + -8s = -24 Add '8s' to each side of the equation. -12r + 4rs + -8s + 8s = -24 + 8s Combine like terms: -8s + 8s = 0 -12r + 4rs + 0 = -24 + 8s -12r + 4rs = -24 + 8s Reorder the terms: 24 + -12r + 4rs + -8s = -24 + 8s + 24 + -8s Reorder the terms: 24 + -12r + 4rs + -8s = -24 + 24 + 8s + -8s Combine like terms: -24 + 24 = 0 24 + -12r + 4rs + -8s = 0 + 8s + -8s 24 + -12r + 4rs + -8s = 8s + -8s Combine like terms: 8s + -8s = 0 24 + -12r + 4rs + -8s = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -3r + rs + -2s) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + -3r + rs + -2s)' equal to zero and attempt to solve: Simplifying 6 + -3r + rs + -2s = 0 Solving 6 + -3r + rs + -2s = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -3r + rs + -6 + -2s = 0 + -6 Reorder the terms: 6 + -6 + -3r + rs + -2s = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -3r + rs + -2s = 0 + -6 -3r + rs + -2s = 0 + -6 Combine like terms: 0 + -6 = -6 -3r + rs + -2s = -6 Add '2s' to each side of the equation. -3r + rs + -2s + 2s = -6 + 2s Combine like terms: -2s + 2s = 0 -3r + rs + 0 = -6 + 2s -3r + rs = -6 + 2s 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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