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Simplifying
(6y + -7z)(6y + 7z) = 0
Multiply (6y + -7z) * (6y + 7z)
(6y * (6y + 7z) + -7z * (6y + 7z)) = 0
((6y * 6y + 7z * 6y) + -7z * (6y + 7z)) = 0
Reorder the terms:
((42yz + 36y2) + -7z * (6y + 7z)) = 0
((42yz + 36y2) + -7z * (6y + 7z)) = 0
(42yz + 36y2 + (6y * -7z + 7z * -7z)) = 0
(42yz + 36y2 + (-42yz + -49z2)) = 0
Reorder the terms:
(42yz + -42yz + 36y2 + -49z2) = 0
Combine like terms: 42yz + -42yz = 0
(0 + 36y2 + -49z2) = 0
(36y2 + -49z2) = 0
Solving
36y2 + -49z2 = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '49z2' to each side of the equation.
36y2 + -49z2 + 49z2 = 0 + 49z2
Combine like terms: -49z2 + 49z2 = 0
36y2 + 0 = 0 + 49z2
36y2 = 0 + 49z2
Remove the zero:
36y2 = 49z2
Divide each side by '36'.
y2 = 1.361111111z2
Simplifying
y2 = 1.361111111z2
Take the square root of each side:
y = {-1.166666667z, 1.166666667z}
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