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Simplifying (3C + 5s)(7s + -7c) = 0 Reorder the terms: (3C + 5s)(-7c + 7s) = 0 Multiply (3C + 5s) * (-7c + 7s) (3C * (-7c + 7s) + 5s * (-7c + 7s)) = 0 ((-7c * 3C + 7s * 3C) + 5s * (-7c + 7s)) = 0 ((-21cC + 21sC) + 5s * (-7c + 7s)) = 0 (-21cC + 21sC + (-7c * 5s + 7s * 5s)) = 0 (-21cC + 21sC + (-35cs + 35s2)) = 0 Reorder the terms: (-21cC + -35cs + 21sC + 35s2) = 0 (-21cC + -35cs + 21sC + 35s2) = 0 Solving -21cC + -35cs + 21sC + 35s2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-21sC' to each side of the equation. -21cC + -35cs + 21sC + -21sC + 35s2 = 0 + -21sC Combine like terms: 21sC + -21sC = 0 -21cC + -35cs + 0 + 35s2 = 0 + -21sC -21cC + -35cs + 35s2 = 0 + -21sC Remove the zero: -21cC + -35cs + 35s2 = -21sC Add '-35s2' to each side of the equation. -21cC + -35cs + 35s2 + -35s2 = -21sC + -35s2 Combine like terms: 35s2 + -35s2 = 0 -21cC + -35cs + 0 = -21sC + -35s2 -21cC + -35cs = -21sC + -35s2 Reorder the terms: -21cC + -35cs + 21sC + 35s2 = -21sC + 21sC + -35s2 + 35s2 Combine like terms: -21sC + 21sC = 0 -21cC + -35cs + 21sC + 35s2 = 0 + -35s2 + 35s2 -21cC + -35cs + 21sC + 35s2 = -35s2 + 35s2 Combine like terms: -35s2 + 35s2 = 0 -21cC + -35cs + 21sC + 35s2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-3cC + -5cs + 3sC + 5s2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-3cC + -5cs + 3sC + 5s2)' equal to zero and attempt to solve: Simplifying -3cC + -5cs + 3sC + 5s2 = 0 Solving -3cC + -5cs + 3sC + 5s2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-3sC' to each side of the equation. -3cC + -5cs + 3sC + -3sC + 5s2 = 0 + -3sC Combine like terms: 3sC + -3sC = 0 -3cC + -5cs + 0 + 5s2 = 0 + -3sC -3cC + -5cs + 5s2 = 0 + -3sC Remove the zero: -3cC + -5cs + 5s2 = -3sC Add '-5s2' to each side of the equation. -3cC + -5cs + 5s2 + -5s2 = -3sC + -5s2 Combine like terms: 5s2 + -5s2 = 0 -3cC + -5cs + 0 = -3sC + -5s2 -3cC + -5cs = -3sC + -5s2 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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