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Simplifying 3x2 + 6x + -1(2k + 3) = 0 Reorder the terms: 3x2 + 6x + -1(3 + 2k) = 0 3x2 + 6x + (3 * -1 + 2k * -1) = 0 3x2 + 6x + (-3 + -2k) = 0 Reorder the terms: -3 + -2k + 6x + 3x2 = 0 Solving -3 + -2k + 6x + 3x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -2k + 6x + 3 + 3x2 = 0 + 3 Reorder the terms: -3 + 3 + -2k + 6x + 3x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2k + 6x + 3x2 = 0 + 3 -2k + 6x + 3x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -2k + 6x + 3x2 = 3 Add '-6x' to each side of the equation. -2k + 6x + -6x + 3x2 = 3 + -6x Combine like terms: 6x + -6x = 0 -2k + 0 + 3x2 = 3 + -6x -2k + 3x2 = 3 + -6x Add '-3x2' to each side of the equation. -2k + 3x2 + -3x2 = 3 + -6x + -3x2 Combine like terms: 3x2 + -3x2 = 0 -2k + 0 = 3 + -6x + -3x2 -2k = 3 + -6x + -3x2 Divide each side by '-2'. k = -1.5 + 3x + 1.5x2 Simplifying k = -1.5 + 3x + 1.5x2
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