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Simplifying (3h + 4)(6h + 9) * h = h(3h + 4)(2l + 1) Reorder the terms: (4 + 3h)(6h + 9) * h = h(3h + 4)(2l + 1) Reorder the terms: (4 + 3h)(9 + 6h) * h = h(3h + 4)(2l + 1) Reorder the terms for easier multiplication: h(4 + 3h)(9 + 6h) = h(3h + 4)(2l + 1) Multiply (4 + 3h) * (9 + 6h) h(4(9 + 6h) + 3h * (9 + 6h)) = h(3h + 4)(2l + 1) h((9 * 4 + 6h * 4) + 3h * (9 + 6h)) = h(3h + 4)(2l + 1) h((36 + 24h) + 3h * (9 + 6h)) = h(3h + 4)(2l + 1) h(36 + 24h + (9 * 3h + 6h * 3h)) = h(3h + 4)(2l + 1) h(36 + 24h + (27h + 18h2)) = h(3h + 4)(2l + 1) Combine like terms: 24h + 27h = 51h h(36 + 51h + 18h2) = h(3h + 4)(2l + 1) (36 * h + 51h * h + 18h2 * h) = h(3h + 4)(2l + 1) (36h + 51h2 + 18h3) = h(3h + 4)(2l + 1) Reorder the terms: 36h + 51h2 + 18h3 = h(4 + 3h)(2l + 1) Reorder the terms: 36h + 51h2 + 18h3 = h(4 + 3h)(1 + 2l) Multiply (4 + 3h) * (1 + 2l) 36h + 51h2 + 18h3 = h(4(1 + 2l) + 3h * (1 + 2l)) 36h + 51h2 + 18h3 = h((1 * 4 + 2l * 4) + 3h * (1 + 2l)) 36h + 51h2 + 18h3 = h((4 + 8l) + 3h * (1 + 2l)) 36h + 51h2 + 18h3 = h(4 + 8l + (1 * 3h + 2l * 3h)) 36h + 51h2 + 18h3 = h(4 + 8l + (3h + 6hl)) Reorder the terms: 36h + 51h2 + 18h3 = h(4 + 3h + 6hl + 8l) 36h + 51h2 + 18h3 = h(4 + 3h + 6hl + 8l) 36h + 51h2 + 18h3 = (4 * h + 3h * h + 6hl * h + 8l * h) Reorder the terms: 36h + 51h2 + 18h3 = (4h + 8hl + 3h2 + 6h2l) 36h + 51h2 + 18h3 = (4h + 8hl + 3h2 + 6h2l) Solving 36h + 51h2 + 18h3 = 4h + 8hl + 3h2 + 6h2l Solving for variable 'h'. Reorder the terms: 36h + -4h + -8hl + 51h2 + -3h2 + -6h2l + 18h3 = 4h + 8hl + 3h2 + 6h2l + -4h + -8hl + -3h2 + -6h2l Combine like terms: 36h + -4h = 32h 32h + -8hl + 51h2 + -3h2 + -6h2l + 18h3 = 4h + 8hl + 3h2 + 6h2l + -4h + -8hl + -3h2 + -6h2l Combine like terms: 51h2 + -3h2 = 48h2 32h + -8hl + 48h2 + -6h2l + 18h3 = 4h + 8hl + 3h2 + 6h2l + -4h + -8hl + -3h2 + -6h2l Reorder the terms: 32h + -8hl + 48h2 + -6h2l + 18h3 = 4h + -4h + 8hl + -8hl + 3h2 + -3h2 + 6h2l + -6h2l Combine like terms: 4h + -4h = 0 32h + -8hl + 48h2 + -6h2l + 18h3 = 0 + 8hl + -8hl + 3h2 + -3h2 + 6h2l + -6h2l 32h + -8hl + 48h2 + -6h2l + 18h3 = 8hl + -8hl + 3h2 + -3h2 + 6h2l + -6h2l Combine like terms: 8hl + -8hl = 0 32h + -8hl + 48h2 + -6h2l + 18h3 = 0 + 3h2 + -3h2 + 6h2l + -6h2l 32h + -8hl + 48h2 + -6h2l + 18h3 = 3h2 + -3h2 + 6h2l + -6h2l Combine like terms: 3h2 + -3h2 = 0 32h + -8hl + 48h2 + -6h2l + 18h3 = 0 + 6h2l + -6h2l 32h + -8hl + 48h2 + -6h2l + 18h3 = 6h2l + -6h2l Combine like terms: 6h2l + -6h2l = 0 32h + -8hl + 48h2 + -6h2l + 18h3 = 0 Factor out the Greatest Common Factor (GCF), '2h'. 2h(16 + -4l + 24h + -3hl + 9h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'h' equal to zero and attempt to solve: Simplifying h = 0 Solving h = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h = 0Subproblem 2
Set the factor '(16 + -4l + 24h + -3hl + 9h2)' equal to zero and attempt to solve: Simplifying 16 + -4l + 24h + -3hl + 9h2 = 0 Reorder the terms: 16 + 24h + -3hl + 9h2 + -4l = 0 Solving 16 + 24h + -3hl + 9h2 + -4l = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
h = {0}
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