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Simplifying (10c + 7)(3c + -5) = 0 Reorder the terms: (7 + 10c)(3c + -5) = 0 Reorder the terms: (7 + 10c)(-5 + 3c) = 0 Multiply (7 + 10c) * (-5 + 3c) (7(-5 + 3c) + 10c * (-5 + 3c)) = 0 ((-5 * 7 + 3c * 7) + 10c * (-5 + 3c)) = 0 ((-35 + 21c) + 10c * (-5 + 3c)) = 0 (-35 + 21c + (-5 * 10c + 3c * 10c)) = 0 (-35 + 21c + (-50c + 30c2)) = 0 Combine like terms: 21c + -50c = -29c (-35 + -29c + 30c2) = 0 Solving -35 + -29c + 30c2 = 0 Solving for variable 'c'. Factor a trinomial. (-7 + -10c)(5 + -3c) = 0Subproblem 1
Set the factor '(-7 + -10c)' equal to zero and attempt to solve: Simplifying -7 + -10c = 0 Solving -7 + -10c = 0 Move all terms containing c to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -10c = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10c = 0 + 7 -10c = 0 + 7 Combine like terms: 0 + 7 = 7 -10c = 7 Divide each side by '-10'. c = -0.7 Simplifying c = -0.7Subproblem 2
Set the factor '(5 + -3c)' equal to zero and attempt to solve: Simplifying 5 + -3c = 0 Solving 5 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3c = 0 + -5 -3c = 0 + -5 Combine like terms: 0 + -5 = -5 -3c = -5 Divide each side by '-3'. c = 1.666666667 Simplifying c = 1.666666667Solution
c = {-0.7, 1.666666667}
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