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Simplifying (5c + -3)(4c + 7) = 0 Reorder the terms: (-3 + 5c)(4c + 7) = 0 Reorder the terms: (-3 + 5c)(7 + 4c) = 0 Multiply (-3 + 5c) * (7 + 4c) (-3(7 + 4c) + 5c * (7 + 4c)) = 0 ((7 * -3 + 4c * -3) + 5c * (7 + 4c)) = 0 ((-21 + -12c) + 5c * (7 + 4c)) = 0 (-21 + -12c + (7 * 5c + 4c * 5c)) = 0 (-21 + -12c + (35c + 20c2)) = 0 Combine like terms: -12c + 35c = 23c (-21 + 23c + 20c2) = 0 Solving -21 + 23c + 20c2 = 0 Solving for variable 'c'. Factor a trinomial. (-7 + -4c)(3 + -5c) = 0Subproblem 1
Set the factor '(-7 + -4c)' equal to zero and attempt to solve: Simplifying -7 + -4c = 0 Solving -7 + -4c = 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 + -4c = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4c = 0 + 7 -4c = 0 + 7 Combine like terms: 0 + 7 = 7 -4c = 7 Divide each side by '-4'. c = -1.75 Simplifying c = -1.75Subproblem 2
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 = 0.6Solution
c = {-1.75, 0.6}
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