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Simplifying (4c + -10)(c + -4) = 0 Reorder the terms: (-10 + 4c)(c + -4) = 0 Reorder the terms: (-10 + 4c)(-4 + c) = 0 Multiply (-10 + 4c) * (-4 + c) (-10(-4 + c) + 4c * (-4 + c)) = 0 ((-4 * -10 + c * -10) + 4c * (-4 + c)) = 0 ((40 + -10c) + 4c * (-4 + c)) = 0 (40 + -10c + (-4 * 4c + c * 4c)) = 0 (40 + -10c + (-16c + 4c2)) = 0 Combine like terms: -10c + -16c = -26c (40 + -26c + 4c2) = 0 Solving 40 + -26c + 4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + -13c + 2c2) = 0 Factor a trinomial. 2((5 + -2c)(4 + -1c)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2c)' equal to zero and attempt to solve: Simplifying 5 + -2c = 0 Solving 5 + -2c = 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 + -2c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2c = 0 + -5 -2c = 0 + -5 Combine like terms: 0 + -5 = -5 -2c = -5 Divide each side by '-2'. c = 2.5 Simplifying c = 2.5Subproblem 2
Set the factor '(4 + -1c)' equal to zero and attempt to solve: Simplifying 4 + -1c = 0 Solving 4 + -1c = 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 + -1c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1c = 0 + -4 -1c = 0 + -4 Combine like terms: 0 + -4 = -4 -1c = -4 Divide each side by '-1'. c = 4 Simplifying c = 4Solution
c = {2.5, 4}
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