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Simplifying 12z2 + 7xz + -12x2 = 0 Reorder the terms: 7xz + -12x2 + 12z2 = 0 Solving 7xz + -12x2 + 12z2 = 0 Solving for variable 'x'. Factor a trinomial. (-4x + -3z)(3x + -4z) = 0Subproblem 1
Set the factor '(-4x + -3z)' equal to zero and attempt to solve: Simplifying -4x + -3z = 0 Solving -4x + -3z = 0 Move all terms containing x to the left, all other terms to the right. Add '3z' to each side of the equation. -4x + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 -4x + 0 = 0 + 3z -4x = 0 + 3z Remove the zero: -4x = 3z Divide each side by '-4'. x = -0.75z Simplifying x = -0.75zSubproblem 2
Set the factor '(3x + -4z)' equal to zero and attempt to solve: Simplifying 3x + -4z = 0 Solving 3x + -4z = 0 Move all terms containing x to the left, all other terms to the right. Add '4z' to each side of the equation. 3x + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 3x + 0 = 0 + 4z 3x = 0 + 4z Remove the zero: 3x = 4z Divide each side by '3'. x = 1.333333333z Simplifying x = 1.333333333zSolution
x = {-0.75z, 1.333333333z}
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