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Simplifying H(x) = -3x2 + -12x Multiply H * x xH = -3x2 + -12x Reorder the terms: xH = -12x + -3x2 Solving xH = -12x + -3x2 Solving for variable 'x'. Reorder the terms: 12x + xH + 3x2 = -12x + -3x2 + 12x + 3x2 Reorder the terms: 12x + xH + 3x2 = -12x + 12x + -3x2 + 3x2 Combine like terms: -12x + 12x = 0 12x + xH + 3x2 = 0 + -3x2 + 3x2 12x + xH + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 12x + xH + 3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + H + 3x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(12 + H + 3x)' equal to zero and attempt to solve: Simplifying 12 + H + 3x = 0 Solving 12 + H + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + H + -12 + 3x = 0 + -12 Reorder the terms: 12 + -12 + H + 3x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + H + 3x = 0 + -12 H + 3x = 0 + -12 Combine like terms: 0 + -12 = -12 H + 3x = -12 Add '-1H' to each side of the equation. H + -1H + 3x = -12 + -1H Combine like terms: H + -1H = 0 0 + 3x = -12 + -1H 3x = -12 + -1H Divide each side by '3'. x = -4 + -0.3333333333H Simplifying x = -4 + -0.3333333333HSolution
x = {0, -4 + -0.3333333333H}
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