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Simplifying 6x2 + -15xz + -9z2 = 0 Reorder the terms: -15xz + 6x2 + -9z2 = 0 Solving -15xz + 6x2 + -9z2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5xz + 2x2 + -3z2) = 0 Factor a trinomial. 3((x + -3z)(2x + z)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + -3z)' equal to zero and attempt to solve: Simplifying x + -3z = 0 Solving x + -3z = 0 Move all terms containing x to the left, all other terms to the right. Add '3z' to each side of the equation. x + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 x + 0 = 0 + 3z x = 0 + 3z Remove the zero: x = 3z Simplifying x = 3zSubproblem 2
Set the factor '(2x + z)' equal to zero and attempt to solve: Simplifying 2x + z = 0 Solving 2x + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1z' to each side of the equation. 2x + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 2x + 0 = 0 + -1z 2x = 0 + -1z Remove the zero: 2x = -1z Divide each side by '2'. x = -0.5z Simplifying x = -0.5zSolution
x = {3z, -0.5z}
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