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Simplifying (-8c + 3)(-4c + 3) = 0 Reorder the terms: (3 + -8c)(-4c + 3) = 0 Reorder the terms: (3 + -8c)(3 + -4c) = 0 Multiply (3 + -8c) * (3 + -4c) (3(3 + -4c) + -8c * (3 + -4c)) = 0 ((3 * 3 + -4c * 3) + -8c * (3 + -4c)) = 0 ((9 + -12c) + -8c * (3 + -4c)) = 0 (9 + -12c + (3 * -8c + -4c * -8c)) = 0 (9 + -12c + (-24c + 32c2)) = 0 Combine like terms: -12c + -24c = -36c (9 + -36c + 32c2) = 0 Solving 9 + -36c + 32c2 = 0 Solving for variable 'c'. Factor a trinomial. (3 + -8c)(3 + -4c) = 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 '(3 + -4c)' equal to zero and attempt to solve: Simplifying 3 + -4c = 0 Solving 3 + -4c = 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 + -4c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4c = 0 + -3 -4c = 0 + -3 Combine like terms: 0 + -3 = -3 -4c = -3 Divide each side by '-4'. c = 0.75 Simplifying c = 0.75Solution
c = {0.375, 0.75}
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