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Simplifying
(4x + -8z)(4x + 8z) = 0
Multiply (4x + -8z) * (4x + 8z)
(4x * (4x + 8z) + -8z * (4x + 8z)) = 0
((4x * 4x + 8z * 4x) + -8z * (4x + 8z)) = 0
Reorder the terms:
((32xz + 16x2) + -8z * (4x + 8z)) = 0
((32xz + 16x2) + -8z * (4x + 8z)) = 0
(32xz + 16x2 + (4x * -8z + 8z * -8z)) = 0
(32xz + 16x2 + (-32xz + -64z2)) = 0
Reorder the terms:
(32xz + -32xz + 16x2 + -64z2) = 0
Combine like terms: 32xz + -32xz = 0
(0 + 16x2 + -64z2) = 0
(16x2 + -64z2) = 0
Solving
16x2 + -64z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '64z2' to each side of the equation.
16x2 + -64z2 + 64z2 = 0 + 64z2
Combine like terms: -64z2 + 64z2 = 0
16x2 + 0 = 0 + 64z2
16x2 = 0 + 64z2
Remove the zero:
16x2 = 64z2
Divide each side by '16'.
x2 = 4z2
Simplifying
x2 = 4z2
Take the square root of each side:
x = {-2z, 2z}
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