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Simplifying (3x + -4z)(5x + -7z) = 0 Multiply (3x + -4z) * (5x + -7z) (3x * (5x + -7z) + -4z * (5x + -7z)) = 0 ((5x * 3x + -7z * 3x) + -4z * (5x + -7z)) = 0 Reorder the terms: ((-21xz + 15x2) + -4z * (5x + -7z)) = 0 ((-21xz + 15x2) + -4z * (5x + -7z)) = 0 (-21xz + 15x2 + (5x * -4z + -7z * -4z)) = 0 (-21xz + 15x2 + (-20xz + 28z2)) = 0 Reorder the terms: (-21xz + -20xz + 15x2 + 28z2) = 0 Combine like terms: -21xz + -20xz = -41xz (-41xz + 15x2 + 28z2) = 0 Solving -41xz + 15x2 + 28z2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -7z)(3x + -4z) = 0Subproblem 1
Set the factor '(5x + -7z)' equal to zero and attempt to solve: Simplifying 5x + -7z = 0 Solving 5x + -7z = 0 Move all terms containing x to the left, all other terms to the right. Add '7z' to each side of the equation. 5x + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 5x + 0 = 0 + 7z 5x = 0 + 7z Remove the zero: 5x = 7z Divide each side by '5'. x = 1.4z Simplifying x = 1.4zSubproblem 2
Set the factor '(3x + -4z)' equal to zero and attempt to solve: Simplifying 3x + -4z = 0 Solving 3x + -4z = 0 Move all terms containing x to the left, all other terms to the right. Add '4z' to each side of the equation. 3x + -4z + 4z = 0 + 4z Combine like terms: -4z + 4z = 0 3x + 0 = 0 + 4z 3x = 0 + 4z Remove the zero: 3x = 4z Divide each side by '3'. x = 1.333333333z Simplifying x = 1.333333333zSolution
x = {1.4z, 1.333333333z}
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