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Simplifying (4x + -1z)(6x + -7z) = 0 Multiply (4x + -1z) * (6x + -7z) (4x * (6x + -7z) + -1z * (6x + -7z)) = 0 ((6x * 4x + -7z * 4x) + -1z * (6x + -7z)) = 0 Reorder the terms: ((-28xz + 24x2) + -1z * (6x + -7z)) = 0 ((-28xz + 24x2) + -1z * (6x + -7z)) = 0 (-28xz + 24x2 + (6x * -1z + -7z * -1z)) = 0 (-28xz + 24x2 + (-6xz + 7z2)) = 0 Reorder the terms: (-28xz + -6xz + 24x2 + 7z2) = 0 Combine like terms: -28xz + -6xz = -34xz (-34xz + 24x2 + 7z2) = 0 Solving -34xz + 24x2 + 7z2 = 0 Solving for variable 'x'. Factor a trinomial. (6x + -7z)(4x + -1z) = 0Subproblem 1
Set the factor '(6x + -7z)' equal to zero and attempt to solve: Simplifying 6x + -7z = 0 Solving 6x + -7z = 0 Move all terms containing x to the left, all other terms to the right. Add '7z' to each side of the equation. 6x + -7z + 7z = 0 + 7z Combine like terms: -7z + 7z = 0 6x + 0 = 0 + 7z 6x = 0 + 7z Remove the zero: 6x = 7z Divide each side by '6'. x = 1.166666667z Simplifying x = 1.166666667zSubproblem 2
Set the factor '(4x + -1z)' equal to zero and attempt to solve: Simplifying 4x + -1z = 0 Solving 4x + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add 'z' to each side of the equation. 4x + -1z + z = 0 + z Combine like terms: -1z + z = 0 4x + 0 = 0 + z 4x = 0 + z Remove the zero: 4x = z Divide each side by '4'. x = 0.25z Simplifying x = 0.25zSolution
x = {1.166666667z, 0.25z}
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