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Simplifying (3x + -1z)(8x + -3z) = 0 Multiply (3x + -1z) * (8x + -3z) (3x * (8x + -3z) + -1z * (8x + -3z)) = 0 ((8x * 3x + -3z * 3x) + -1z * (8x + -3z)) = 0 Reorder the terms: ((-9xz + 24x2) + -1z * (8x + -3z)) = 0 ((-9xz + 24x2) + -1z * (8x + -3z)) = 0 (-9xz + 24x2 + (8x * -1z + -3z * -1z)) = 0 (-9xz + 24x2 + (-8xz + 3z2)) = 0 Reorder the terms: (-9xz + -8xz + 24x2 + 3z2) = 0 Combine like terms: -9xz + -8xz = -17xz (-17xz + 24x2 + 3z2) = 0 Solving -17xz + 24x2 + 3z2 = 0 Solving for variable 'x'. Factor a trinomial. (8x + -3z)(3x + -1z) = 0Subproblem 1
Set the factor '(8x + -3z)' equal to zero and attempt to solve: Simplifying 8x + -3z = 0 Solving 8x + -3z = 0 Move all terms containing x to the left, all other terms to the right. Add '3z' to each side of the equation. 8x + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 8x + 0 = 0 + 3z 8x = 0 + 3z Remove the zero: 8x = 3z Divide each side by '8'. x = 0.375z Simplifying x = 0.375zSubproblem 2
Set the factor '(3x + -1z)' equal to zero and attempt to solve: Simplifying 3x + -1z = 0 Solving 3x + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add 'z' to each side of the equation. 3x + -1z + z = 0 + z Combine like terms: -1z + z = 0 3x + 0 = 0 + z 3x = 0 + z Remove the zero: 3x = z Divide each side by '3'. x = 0.3333333333z Simplifying x = 0.3333333333zSolution
x = {0.375z, 0.3333333333z}
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