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Simplifying (5x + -1z)(4x + z) = 0 Multiply (5x + -1z) * (4x + z) (5x * (4x + z) + -1z * (4x + z)) = 0 ((4x * 5x + z * 5x) + -1z * (4x + z)) = 0 Reorder the terms: ((5xz + 20x2) + -1z * (4x + z)) = 0 ((5xz + 20x2) + -1z * (4x + z)) = 0 (5xz + 20x2 + (4x * -1z + z * -1z)) = 0 (5xz + 20x2 + (-4xz + -1z2)) = 0 Reorder the terms: (5xz + -4xz + 20x2 + -1z2) = 0 Combine like terms: 5xz + -4xz = 1xz (1xz + 20x2 + -1z2) = 0 Solving 1xz + 20x2 + -1z2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -1z)(4x + z) = 0Subproblem 1
Set the factor '(5x + -1z)' equal to zero and attempt to solve: Simplifying 5x + -1z = 0 Solving 5x + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add 'z' to each side of the equation. 5x + -1z + z = 0 + z Combine like terms: -1z + z = 0 5x + 0 = 0 + z 5x = 0 + z Remove the zero: 5x = z Divide each side by '5'. x = 0.2z Simplifying x = 0.2zSubproblem 2
Set the factor '(4x + z)' equal to zero and attempt to solve: Simplifying 4x + z = 0 Solving 4x + z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1z' to each side of the equation. 4x + z + -1z = 0 + -1z Combine like terms: z + -1z = 0 4x + 0 = 0 + -1z 4x = 0 + -1z Remove the zero: 4x = -1z Divide each side by '4'. x = -0.25z Simplifying x = -0.25zSolution
x = {0.2z, -0.25z}
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