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Simplifying
(6x + -3z)(6x + 3z) = 0
Multiply (6x + -3z) * (6x + 3z)
(6x * (6x + 3z) + -3z * (6x + 3z)) = 0
((6x * 6x + 3z * 6x) + -3z * (6x + 3z)) = 0
Reorder the terms:
((18xz + 36x2) + -3z * (6x + 3z)) = 0
((18xz + 36x2) + -3z * (6x + 3z)) = 0
(18xz + 36x2 + (6x * -3z + 3z * -3z)) = 0
(18xz + 36x2 + (-18xz + -9z2)) = 0
Reorder the terms:
(18xz + -18xz + 36x2 + -9z2) = 0
Combine like terms: 18xz + -18xz = 0
(0 + 36x2 + -9z2) = 0
(36x2 + -9z2) = 0
Solving
36x2 + -9z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9z2' to each side of the equation.
36x2 + -9z2 + 9z2 = 0 + 9z2
Combine like terms: -9z2 + 9z2 = 0
36x2 + 0 = 0 + 9z2
36x2 = 0 + 9z2
Remove the zero:
36x2 = 9z2
Divide each side by '36'.
x2 = 0.25z2
Simplifying
x2 = 0.25z2
Take the square root of each side:
x = {-0.5z, 0.5z}
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