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Simplifying
(3x + -8z)(3x + 8z) = 0
Multiply (3x + -8z) * (3x + 8z)
(3x * (3x + 8z) + -8z * (3x + 8z)) = 0
((3x * 3x + 8z * 3x) + -8z * (3x + 8z)) = 0
Reorder the terms:
((24xz + 9x2) + -8z * (3x + 8z)) = 0
((24xz + 9x2) + -8z * (3x + 8z)) = 0
(24xz + 9x2 + (3x * -8z + 8z * -8z)) = 0
(24xz + 9x2 + (-24xz + -64z2)) = 0
Reorder the terms:
(24xz + -24xz + 9x2 + -64z2) = 0
Combine like terms: 24xz + -24xz = 0
(0 + 9x2 + -64z2) = 0
(9x2 + -64z2) = 0
Solving
9x2 + -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.
9x2 + -64z2 + 64z2 = 0 + 64z2
Combine like terms: -64z2 + 64z2 = 0
9x2 + 0 = 0 + 64z2
9x2 = 0 + 64z2
Remove the zero:
9x2 = 64z2
Divide each side by '9'.
x2 = 7.111111111z2
Simplifying
x2 = 7.111111111z2
Take the square root of each side:
x = {-2.666666667z, 2.666666667z}
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