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Simplifying (5c + 3)(6c + -7) = 0 Reorder the terms: (3 + 5c)(6c + -7) = 0 Reorder the terms: (3 + 5c)(-7 + 6c) = 0 Multiply (3 + 5c) * (-7 + 6c) (3(-7 + 6c) + 5c * (-7 + 6c)) = 0 ((-7 * 3 + 6c * 3) + 5c * (-7 + 6c)) = 0 ((-21 + 18c) + 5c * (-7 + 6c)) = 0 (-21 + 18c + (-7 * 5c + 6c * 5c)) = 0 (-21 + 18c + (-35c + 30c2)) = 0 Combine like terms: 18c + -35c = -17c (-21 + -17c + 30c2) = 0 Solving -21 + -17c + 30c2 = 0 Solving for variable 'c'. Factor a trinomial. (-3 + -5c)(7 + -6c) = 0Subproblem 1
Set the factor '(-3 + -5c)' equal to zero and attempt to solve: Simplifying -3 + -5c = 0 Solving -3 + -5c = 0 Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5c = 0 + 3 -5c = 0 + 3 Combine like terms: 0 + 3 = 3 -5c = 3 Divide each side by '-5'. c = -0.6 Simplifying c = -0.6Subproblem 2
Set the factor '(7 + -6c)' equal to zero and attempt to solve: Simplifying 7 + -6c = 0 Solving 7 + -6c = 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 + -6c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6c = 0 + -7 -6c = 0 + -7 Combine like terms: 0 + -7 = -7 -6c = -7 Divide each side by '-6'. c = 1.166666667 Simplifying c = 1.166666667Solution
c = {-0.6, 1.166666667}
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