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Simplifying 4x2 + 2xz + -12z2 = 0 Reorder the terms: 2xz + 4x2 + -12z2 = 0 Solving 2xz + 4x2 + -12z2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(xz + 2x2 + -6z2) = 0 Factor a trinomial. 2((2x + -3z)(x + 2z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2x + -3z)' equal to zero and attempt to solve: Simplifying 2x + -3z = 0 Solving 2x + -3z = 0 Move all terms containing x to the left, all other terms to the right. Add '3z' to each side of the equation. 2x + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 2x + 0 = 0 + 3z 2x = 0 + 3z Remove the zero: 2x = 3z Divide each side by '2'. x = 1.5z Simplifying x = 1.5zSubproblem 2
Set the factor '(x + 2z)' equal to zero and attempt to solve: Simplifying x + 2z = 0 Solving x + 2z = 0 Move all terms containing x to the left, all other terms to the right. Add '-2z' to each side of the equation. x + 2z + -2z = 0 + -2z Combine like terms: 2z + -2z = 0 x + 0 = 0 + -2z x = 0 + -2z Remove the zero: x = -2z Simplifying x = -2zSolution
x = {1.5z, -2z}
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