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Simplifying 30x2 + -13xc + -3c2 = 0 Reorder the terms: -13cx + -3c2 + 30x2 = 0 Solving -13cx + -3c2 + 30x2 = 0 Solving for variable 'c'. Factor a trinomial. (-1c + -6x)(3c + -5x) = 0Subproblem 1
Set the factor '(-1c + -6x)' equal to zero and attempt to solve: Simplifying -1c + -6x = 0 Solving -1c + -6x = 0 Move all terms containing c to the left, all other terms to the right. Add '6x' to each side of the equation. -1c + -6x + 6x = 0 + 6x Combine like terms: -6x + 6x = 0 -1c + 0 = 0 + 6x -1c = 0 + 6x Remove the zero: -1c = 6x Divide each side by '-1'. c = -6x Simplifying c = -6xSubproblem 2
Set the factor '(3c + -5x)' equal to zero and attempt to solve: Simplifying 3c + -5x = 0 Solving 3c + -5x = 0 Move all terms containing c to the left, all other terms to the right. Add '5x' to each side of the equation. 3c + -5x + 5x = 0 + 5x Combine like terms: -5x + 5x = 0 3c + 0 = 0 + 5x 3c = 0 + 5x Remove the zero: 3c = 5x Divide each side by '3'. c = 1.666666667x Simplifying c = 1.666666667xSolution
c = {-6x, 1.666666667x}
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