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Simplifying (8c + 3)(5c + -4) = 0 Reorder the terms: (3 + 8c)(5c + -4) = 0 Reorder the terms: (3 + 8c)(-4 + 5c) = 0 Multiply (3 + 8c) * (-4 + 5c) (3(-4 + 5c) + 8c * (-4 + 5c)) = 0 ((-4 * 3 + 5c * 3) + 8c * (-4 + 5c)) = 0 ((-12 + 15c) + 8c * (-4 + 5c)) = 0 (-12 + 15c + (-4 * 8c + 5c * 8c)) = 0 (-12 + 15c + (-32c + 40c2)) = 0 Combine like terms: 15c + -32c = -17c (-12 + -17c + 40c2) = 0 Solving -12 + -17c + 40c2 = 0 Solving for variable 'c'. Factor a trinomial. (-3 + -8c)(4 + -5c) = 0Subproblem 1
Set the factor '(-3 + -8c)' equal to zero and attempt to solve: Simplifying -3 + -8c = 0 Solving -3 + -8c = 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 + -8c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8c = 0 + 3 -8c = 0 + 3 Combine like terms: 0 + 3 = 3 -8c = 3 Divide each side by '-8'. c = -0.375 Simplifying c = -0.375Subproblem 2
Set the factor '(4 + -5c)' equal to zero and attempt to solve: Simplifying 4 + -5c = 0 Solving 4 + -5c = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -5c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5c = 0 + -4 -5c = 0 + -4 Combine like terms: 0 + -4 = -4 -5c = -4 Divide each side by '-5'. c = 0.8 Simplifying c = 0.8Solution
c = {-0.375, 0.8}
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