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Simplifying
(4w + 6z)(4w + -6z) = 0
Multiply (4w + 6z) * (4w + -6z)
(4w * (4w + -6z) + 6z * (4w + -6z)) = 0
((4w * 4w + -6z * 4w) + 6z * (4w + -6z)) = 0
Reorder the terms:
((-24wz + 16w2) + 6z * (4w + -6z)) = 0
((-24wz + 16w2) + 6z * (4w + -6z)) = 0
(-24wz + 16w2 + (4w * 6z + -6z * 6z)) = 0
(-24wz + 16w2 + (24wz + -36z2)) = 0
Reorder the terms:
(-24wz + 24wz + 16w2 + -36z2) = 0
Combine like terms: -24wz + 24wz = 0
(0 + 16w2 + -36z2) = 0
(16w2 + -36z2) = 0
Solving
16w2 + -36z2 = 0
Solving for variable 'w'.
Move all terms containing w to the left, all other terms to the right.
Add '36z2' to each side of the equation.
16w2 + -36z2 + 36z2 = 0 + 36z2
Combine like terms: -36z2 + 36z2 = 0
16w2 + 0 = 0 + 36z2
16w2 = 0 + 36z2
Remove the zero:
16w2 = 36z2
Divide each side by '16'.
w2 = 2.25z2
Simplifying
w2 = 2.25z2
Take the square root of each side:
w = {-1.5z, 1.5z}
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