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Simplifying 3x2 + 4(2k + -1) * x + 12 = 0 Reorder the terms: 3x2 + 4(-1 + 2k) * x + 12 = 0 Reorder the terms for easier multiplication: 3x2 + 4x(-1 + 2k) + 12 = 0 3x2 + (-1 * 4x + 2k * 4x) + 12 = 0 Reorder the terms: 3x2 + (8kx + -4x) + 12 = 0 3x2 + (8kx + -4x) + 12 = 0 Reorder the terms: 12 + 8kx + -4x + 3x2 = 0 Solving 12 + 8kx + -4x + 3x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 8kx + -4x + -12 + 3x2 = 0 + -12 Reorder the terms: 12 + -12 + 8kx + -4x + 3x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 8kx + -4x + 3x2 = 0 + -12 8kx + -4x + 3x2 = 0 + -12 Combine like terms: 0 + -12 = -12 8kx + -4x + 3x2 = -12 Add '4x' to each side of the equation. 8kx + -4x + 4x + 3x2 = -12 + 4x Combine like terms: -4x + 4x = 0 8kx + 0 + 3x2 = -12 + 4x 8kx + 3x2 = -12 + 4x Add '-3x2' to each side of the equation. 8kx + 3x2 + -3x2 = -12 + 4x + -3x2 Combine like terms: 3x2 + -3x2 = 0 8kx + 0 = -12 + 4x + -3x2 8kx = -12 + 4x + -3x2 Divide each side by '8x'. k = -1.5x-1 + 0.5 + -0.375x Simplifying k = -1.5x-1 + 0.5 + -0.375x Reorder the terms: k = 0.5 + -1.5x-1 + -0.375x
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