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Simplifying -7c(5x + -7) * 6(6x) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Reorder the terms: -7c(-7 + 5x) * 6(6x) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Remove parenthesis around (6x) -7c(-7 + 5x) * 6 * 6x + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Reorder the terms for easier multiplication: -7 * 6 * 6c * x(-7 + 5x) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Multiply -7 * 6 -42 * 6c * x(-7 + 5x) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Multiply -42 * 6 -252c * x(-7 + 5x) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Multiply c * x -252cx(-7 + 5x) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 (-7 * -252cx + 5x * -252cx) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 (1764cx + -1260cx2) + 28(5x + -7) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Reorder the terms: 1764cx + -1260cx2 + 28(-7 + 5x) * 10(6x) + -14c(5x + -7) * 4(24) = 0 Remove parenthesis around (6x) 1764cx + -1260cx2 + 28(-7 + 5x) * 10 * 6x + -14c(5x + -7) * 4(24) = 0 Reorder the terms for easier multiplication: 1764cx + -1260cx2 + 28 * 10 * 6x(-7 + 5x) + -14c(5x + -7) * 4(24) = 0 Multiply 28 * 10 1764cx + -1260cx2 + 280 * 6x(-7 + 5x) + -14c(5x + -7) * 4(24) = 0 Multiply 280 * 6 1764cx + -1260cx2 + 1680x(-7 + 5x) + -14c(5x + -7) * 4(24) = 0 1764cx + -1260cx2 + (-7 * 1680x + 5x * 1680x) + -14c(5x + -7) * 4(24) = 0 1764cx + -1260cx2 + (-11760x + 8400x2) + -14c(5x + -7) * 4(24) = 0 Reorder the terms: 1764cx + -1260cx2 + -11760x + 8400x2 + -14c(-7 + 5x) * 4(24) = 0 Reorder the terms for easier multiplication: 1764cx + -1260cx2 + -11760x + 8400x2 + -14 * 4 * 24c(-7 + 5x) = 0 Multiply -14 * 4 1764cx + -1260cx2 + -11760x + 8400x2 + -56 * 24c(-7 + 5x) = 0 Multiply -56 * 24 1764cx + -1260cx2 + -11760x + 8400x2 + -1344c(-7 + 5x) = 0 1764cx + -1260cx2 + -11760x + 8400x2 + (-7 * -1344c + 5x * -1344c) = 0 1764cx + -1260cx2 + -11760x + 8400x2 + (9408c + -6720cx) = 0 Reorder the terms: 9408c + 1764cx + -6720cx + -1260cx2 + -11760x + 8400x2 = 0 Combine like terms: 1764cx + -6720cx = -4956cx 9408c + -4956cx + -1260cx2 + -11760x + 8400x2 = 0 Solving 9408c + -4956cx + -1260cx2 + -11760x + 8400x2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '11760x' to each side of the equation. 9408c + -4956cx + -1260cx2 + -11760x + 11760x + 8400x2 = 0 + 11760x Combine like terms: -11760x + 11760x = 0 9408c + -4956cx + -1260cx2 + 0 + 8400x2 = 0 + 11760x 9408c + -4956cx + -1260cx2 + 8400x2 = 0 + 11760x Remove the zero: 9408c + -4956cx + -1260cx2 + 8400x2 = 11760x Add '-8400x2' to each side of the equation. 9408c + -4956cx + -1260cx2 + 8400x2 + -8400x2 = 11760x + -8400x2 Combine like terms: 8400x2 + -8400x2 = 0 9408c + -4956cx + -1260cx2 + 0 = 11760x + -8400x2 9408c + -4956cx + -1260cx2 = 11760x + -8400x2 Reorder the terms: 9408c + -4956cx + -1260cx2 + -11760x + 8400x2 = 11760x + -11760x + -8400x2 + 8400x2 Combine like terms: 11760x + -11760x = 0 9408c + -4956cx + -1260cx2 + -11760x + 8400x2 = 0 + -8400x2 + 8400x2 9408c + -4956cx + -1260cx2 + -11760x + 8400x2 = -8400x2 + 8400x2 Combine like terms: -8400x2 + 8400x2 = 0 9408c + -4956cx + -1260cx2 + -11760x + 8400x2 = 0 Factor out the Greatest Common Factor (GCF), '84'. 84(112c + -59cx + -15cx2 + -140x + 100x2) = 0 Ignore the factor 84.Subproblem 1
Set the factor '(112c + -59cx + -15cx2 + -140x + 100x2)' equal to zero and attempt to solve: Simplifying 112c + -59cx + -15cx2 + -140x + 100x2 = 0 Solving 112c + -59cx + -15cx2 + -140x + 100x2 = 0 Move all terms containing c to the left, all other terms to the right. Add '140x' to each side of the equation. 112c + -59cx + -15cx2 + -140x + 140x + 100x2 = 0 + 140x Combine like terms: -140x + 140x = 0 112c + -59cx + -15cx2 + 0 + 100x2 = 0 + 140x 112c + -59cx + -15cx2 + 100x2 = 0 + 140x Remove the zero: 112c + -59cx + -15cx2 + 100x2 = 140x Add '-100x2' to each side of the equation. 112c + -59cx + -15cx2 + 100x2 + -100x2 = 140x + -100x2 Combine like terms: 100x2 + -100x2 = 0 112c + -59cx + -15cx2 + 0 = 140x + -100x2 112c + -59cx + -15cx2 = 140x + -100x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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