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Simplifying
(3x + -2z)(3x + 2z) = 0
Multiply (3x + -2z) * (3x + 2z)
(3x * (3x + 2z) + -2z * (3x + 2z)) = 0
((3x * 3x + 2z * 3x) + -2z * (3x + 2z)) = 0
Reorder the terms:
((6xz + 9x2) + -2z * (3x + 2z)) = 0
((6xz + 9x2) + -2z * (3x + 2z)) = 0
(6xz + 9x2 + (3x * -2z + 2z * -2z)) = 0
(6xz + 9x2 + (-6xz + -4z2)) = 0
Reorder the terms:
(6xz + -6xz + 9x2 + -4z2) = 0
Combine like terms: 6xz + -6xz = 0
(0 + 9x2 + -4z2) = 0
(9x2 + -4z2) = 0
Solving
9x2 + -4z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4z2' to each side of the equation.
9x2 + -4z2 + 4z2 = 0 + 4z2
Combine like terms: -4z2 + 4z2 = 0
9x2 + 0 = 0 + 4z2
9x2 = 0 + 4z2
Remove the zero:
9x2 = 4z2
Divide each side by '9'.
x2 = 0.4444444444z2
Simplifying
x2 = 0.4444444444z2
Take the square root of each side:
x = {-0.666666667z, 0.666666667z}
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