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Simplifying (5x + -2z)(5x + 8z) = 0 Multiply (5x + -2z) * (5x + 8z) (5x * (5x + 8z) + -2z * (5x + 8z)) = 0 ((5x * 5x + 8z * 5x) + -2z * (5x + 8z)) = 0 Reorder the terms: ((40xz + 25x2) + -2z * (5x + 8z)) = 0 ((40xz + 25x2) + -2z * (5x + 8z)) = 0 (40xz + 25x2 + (5x * -2z + 8z * -2z)) = 0 (40xz + 25x2 + (-10xz + -16z2)) = 0 Reorder the terms: (40xz + -10xz + 25x2 + -16z2) = 0 Combine like terms: 40xz + -10xz = 30xz (30xz + 25x2 + -16z2) = 0 Solving 30xz + 25x2 + -16z2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -2z)(5x + 8z) = 0Subproblem 1
Set the factor '(5x + -2z)' equal to zero and attempt to solve: Simplifying 5x + -2z = 0 Solving 5x + -2z = 0 Move all terms containing x to the left, all other terms to the right. Add '2z' to each side of the equation. 5x + -2z + 2z = 0 + 2z Combine like terms: -2z + 2z = 0 5x + 0 = 0 + 2z 5x = 0 + 2z Remove the zero: 5x = 2z Divide each side by '5'. x = 0.4z Simplifying x = 0.4zSubproblem 2
Set the factor '(5x + 8z)' equal to zero and attempt to solve: Simplifying 5x + 8z = 0 Solving 5x + 8z = 0 Move all terms containing x to the left, all other terms to the right. Add '-8z' to each side of the equation. 5x + 8z + -8z = 0 + -8z Combine like terms: 8z + -8z = 0 5x + 0 = 0 + -8z 5x = 0 + -8z Remove the zero: 5x = -8z Divide each side by '5'. x = -1.6z Simplifying x = -1.6zSolution
x = {0.4z, -1.6z}
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