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Simplifying 12x2 + -11xyz + -15y2z2 = 0 Reorder the terms: -11xyz + 12x2 + -15y2z2 = 0 Solving -11xyz + 12x2 + -15y2z2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -5yz)(4x + 3yz) = 0Subproblem 1
Set the factor '(3x + -5yz)' equal to zero and attempt to solve: Simplifying 3x + -5yz = 0 Solving 3x + -5yz = 0 Move all terms containing x to the left, all other terms to the right. Add '5yz' to each side of the equation. 3x + -5yz + 5yz = 0 + 5yz Combine like terms: -5yz + 5yz = 0 3x + 0 = 0 + 5yz 3x = 0 + 5yz Remove the zero: 3x = 5yz Divide each side by '3'. x = 1.666666667yz Simplifying x = 1.666666667yzSubproblem 2
Set the factor '(4x + 3yz)' equal to zero and attempt to solve: Simplifying 4x + 3yz = 0 Solving 4x + 3yz = 0 Move all terms containing x to the left, all other terms to the right. Add '-3yz' to each side of the equation. 4x + 3yz + -3yz = 0 + -3yz Combine like terms: 3yz + -3yz = 0 4x + 0 = 0 + -3yz 4x = 0 + -3yz Remove the zero: 4x = -3yz Divide each side by '4'. x = -0.75yz Simplifying x = -0.75yzSolution
x = {1.666666667yz, -0.75yz}
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