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Simplifying (2c + -5)(c + 6) + (c + 6)(3c + -2) = 0 Reorder the terms: (-5 + 2c)(c + 6) + (c + 6)(3c + -2) = 0 Reorder the terms: (-5 + 2c)(6 + c) + (c + 6)(3c + -2) = 0 Multiply (-5 + 2c) * (6 + c) (-5(6 + c) + 2c * (6 + c)) + (c + 6)(3c + -2) = 0 ((6 * -5 + c * -5) + 2c * (6 + c)) + (c + 6)(3c + -2) = 0 ((-30 + -5c) + 2c * (6 + c)) + (c + 6)(3c + -2) = 0 (-30 + -5c + (6 * 2c + c * 2c)) + (c + 6)(3c + -2) = 0 (-30 + -5c + (12c + 2c2)) + (c + 6)(3c + -2) = 0 Combine like terms: -5c + 12c = 7c (-30 + 7c + 2c2) + (c + 6)(3c + -2) = 0 Reorder the terms: -30 + 7c + 2c2 + (6 + c)(3c + -2) = 0 Reorder the terms: -30 + 7c + 2c2 + (6 + c)(-2 + 3c) = 0 Multiply (6 + c) * (-2 + 3c) -30 + 7c + 2c2 + (6(-2 + 3c) + c(-2 + 3c)) = 0 -30 + 7c + 2c2 + ((-2 * 6 + 3c * 6) + c(-2 + 3c)) = 0 -30 + 7c + 2c2 + ((-12 + 18c) + c(-2 + 3c)) = 0 -30 + 7c + 2c2 + (-12 + 18c + (-2 * c + 3c * c)) = 0 -30 + 7c + 2c2 + (-12 + 18c + (-2c + 3c2)) = 0 Combine like terms: 18c + -2c = 16c -30 + 7c + 2c2 + (-12 + 16c + 3c2) = 0 Reorder the terms: -30 + -12 + 7c + 16c + 2c2 + 3c2 = 0 Combine like terms: -30 + -12 = -42 -42 + 7c + 16c + 2c2 + 3c2 = 0 Combine like terms: 7c + 16c = 23c -42 + 23c + 2c2 + 3c2 = 0 Combine like terms: 2c2 + 3c2 = 5c2 -42 + 23c + 5c2 = 0 Solving -42 + 23c + 5c2 = 0 Solving for variable 'c'. Factor a trinomial. (-6 + -1c)(7 + -5c) = 0Subproblem 1
Set the factor '(-6 + -1c)' equal to zero and attempt to solve: Simplifying -6 + -1c = 0 Solving -6 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1c = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1c = 0 + 6 -1c = 0 + 6 Combine like terms: 0 + 6 = 6 -1c = 6 Divide each side by '-1'. c = -6 Simplifying c = -6Subproblem 2
Set the factor '(7 + -5c)' equal to zero and attempt to solve: Simplifying 7 + -5c = 0 Solving 7 + -5c = 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 + -5c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5c = 0 + -7 -5c = 0 + -7 Combine like terms: 0 + -7 = -7 -5c = -7 Divide each side by '-5'. c = 1.4 Simplifying c = 1.4Solution
c = {-6, 1.4}
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