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Simplifying (x + -4)(2x2 + hx + 3) + k = 0 Reorder the terms: (-4 + x)(2x2 + hx + 3) + k = 0 Reorder the terms: (-4 + x)(3 + hx + 2x2) + k = 0 Multiply (-4 + x) * (3 + hx + 2x2) (-4(3 + hx + 2x2) + x(3 + hx + 2x2)) + k = 0 ((3 * -4 + hx * -4 + 2x2 * -4) + x(3 + hx + 2x2)) + k = 0 ((-12 + -4hx + -8x2) + x(3 + hx + 2x2)) + k = 0 (-12 + -4hx + -8x2 + (3 * x + hx * x + 2x2 * x)) + k = 0 Reorder the terms: (-12 + -4hx + -8x2 + (hx2 + 3x + 2x3)) + k = 0 (-12 + -4hx + -8x2 + (hx2 + 3x + 2x3)) + k = 0 Reorder the terms: (-12 + -4hx + hx2 + 3x + -8x2 + 2x3) + k = 0 (-12 + -4hx + hx2 + 3x + -8x2 + 2x3) + k = 0 Reorder the terms: -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 Solving -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -4hx + hx2 + k + 3x + -8x2 + 12 + 2x3 = 0 + 12 Reorder the terms: -12 + 12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + 12 -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + 12 Combine like terms: 0 + 12 = 12 -4hx + hx2 + k + 3x + -8x2 + 2x3 = 12 Add '-1k' to each side of the equation. -4hx + hx2 + k + 3x + -8x2 + -1k + 2x3 = 12 + -1k Reorder the terms: -4hx + hx2 + k + -1k + 3x + -8x2 + 2x3 = 12 + -1k Combine like terms: k + -1k = 0 -4hx + hx2 + 0 + 3x + -8x2 + 2x3 = 12 + -1k -4hx + hx2 + 3x + -8x2 + 2x3 = 12 + -1k Add '-3x' to each side of the equation. -4hx + hx2 + 3x + -8x2 + -3x + 2x3 = 12 + -1k + -3x Reorder the terms: -4hx + hx2 + 3x + -3x + -8x2 + 2x3 = 12 + -1k + -3x Combine like terms: 3x + -3x = 0 -4hx + hx2 + 0 + -8x2 + 2x3 = 12 + -1k + -3x -4hx + hx2 + -8x2 + 2x3 = 12 + -1k + -3x Add '8x2' to each side of the equation. -4hx + hx2 + -8x2 + 8x2 + 2x3 = 12 + -1k + -3x + 8x2 Combine like terms: -8x2 + 8x2 = 0 -4hx + hx2 + 0 + 2x3 = 12 + -1k + -3x + 8x2 -4hx + hx2 + 2x3 = 12 + -1k + -3x + 8x2 Add '-2x3' to each side of the equation. -4hx + hx2 + 2x3 + -2x3 = 12 + -1k + -3x + 8x2 + -2x3 Combine like terms: 2x3 + -2x3 = 0 -4hx + hx2 + 0 = 12 + -1k + -3x + 8x2 + -2x3 -4hx + hx2 = 12 + -1k + -3x + 8x2 + -2x3 Reorder the terms: -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 12 + -1k + -3x + 8x2 + -2x3 + -12 + k + 3x + -8x2 + 2x3 Reorder the terms: -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 12 + -12 + -1k + k + -3x + 3x + 8x2 + -8x2 + -2x3 + 2x3 Combine like terms: 12 + -12 = 0 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + -1k + k + -3x + 3x + 8x2 + -8x2 + -2x3 + 2x3 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = -1k + k + -3x + 3x + 8x2 + -8x2 + -2x3 + 2x3 Combine like terms: -1k + k = 0 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + -3x + 3x + 8x2 + -8x2 + -2x3 + 2x3 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = -3x + 3x + 8x2 + -8x2 + -2x3 + 2x3 Combine like terms: -3x + 3x = 0 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + 8x2 + -8x2 + -2x3 + 2x3 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 8x2 + -8x2 + -2x3 + 2x3 Combine like terms: 8x2 + -8x2 = 0 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 + -2x3 + 2x3 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = -2x3 + 2x3 Combine like terms: -2x3 + 2x3 = 0 -12 + -4hx + hx2 + k + 3x + -8x2 + 2x3 = 0 The solution to this equation could not be determined.
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