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Simplifying (4h + -1k)(2h + 3k) = 0 Multiply (4h + -1k) * (2h + 3k) (4h * (2h + 3k) + -1k * (2h + 3k)) = 0 ((2h * 4h + 3k * 4h) + -1k * (2h + 3k)) = 0 Reorder the terms: ((12hk + 8h2) + -1k * (2h + 3k)) = 0 ((12hk + 8h2) + -1k * (2h + 3k)) = 0 (12hk + 8h2 + (2h * -1k + 3k * -1k)) = 0 (12hk + 8h2 + (-2hk + -3k2)) = 0 Reorder the terms: (12hk + -2hk + 8h2 + -3k2) = 0 Combine like terms: 12hk + -2hk = 10hk (10hk + 8h2 + -3k2) = 0 Solving 10hk + 8h2 + -3k2 = 0 Solving for variable 'h'. Factor a trinomial. (4h + -1k)(2h + 3k) = 0Subproblem 1
Set the factor '(4h + -1k)' equal to zero and attempt to solve: Simplifying 4h + -1k = 0 Solving 4h + -1k = 0 Move all terms containing h to the left, all other terms to the right. Add 'k' to each side of the equation. 4h + -1k + k = 0 + k Combine like terms: -1k + k = 0 4h + 0 = 0 + k 4h = 0 + k Remove the zero: 4h = k Divide each side by '4'. h = 0.25k Simplifying h = 0.25kSubproblem 2
Set the factor '(2h + 3k)' equal to zero and attempt to solve: Simplifying 2h + 3k = 0 Solving 2h + 3k = 0 Move all terms containing h to the left, all other terms to the right. Add '-3k' to each side of the equation. 2h + 3k + -3k = 0 + -3k Combine like terms: 3k + -3k = 0 2h + 0 = 0 + -3k 2h = 0 + -3k Remove the zero: 2h = -3k Divide each side by '2'. h = -1.5k Simplifying h = -1.5kSolution
h = {0.25k, -1.5k}
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