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Simplifying 3x2 + (2k + -1) * x + -2 = 0 Reorder the terms: 3x2 + (-1 + 2k) * x + -2 = 0 Reorder the terms for easier multiplication: 3x2 + x(-1 + 2k) + -2 = 0 3x2 + (-1 * x + 2k * x) + -2 = 0 Reorder the terms: 3x2 + (2kx + -1x) + -2 = 0 3x2 + (2kx + -1x) + -2 = 0 Reorder the terms: -2 + 2kx + -1x + 3x2 = 0 Solving -2 + 2kx + -1x + 3x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2kx + -1x + 2 + 3x2 = 0 + 2 Reorder the terms: -2 + 2 + 2kx + -1x + 3x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2kx + -1x + 3x2 = 0 + 2 2kx + -1x + 3x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2kx + -1x + 3x2 = 2 Add 'x' to each side of the equation. 2kx + -1x + x + 3x2 = 2 + x Combine like terms: -1x + x = 0 2kx + 0 + 3x2 = 2 + x 2kx + 3x2 = 2 + x Add '-3x2' to each side of the equation. 2kx + 3x2 + -3x2 = 2 + x + -3x2 Combine like terms: 3x2 + -3x2 = 0 2kx + 0 = 2 + x + -3x2 2kx = 2 + x + -3x2 Divide each side by '2x'. k = x-1 + 0.5 + -1.5x Simplifying k = x-1 + 0.5 + -1.5x Reorder the terms: k = 0.5 + x-1 + -1.5x
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