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Simplifying
(3a + 4b)(3a + -4b) = 0
Multiply (3a + 4b) * (3a + -4b)
(3a * (3a + -4b) + 4b * (3a + -4b)) = 0
((3a * 3a + -4b * 3a) + 4b * (3a + -4b)) = 0
Reorder the terms:
((-12ab + 9a2) + 4b * (3a + -4b)) = 0
((-12ab + 9a2) + 4b * (3a + -4b)) = 0
(-12ab + 9a2 + (3a * 4b + -4b * 4b)) = 0
(-12ab + 9a2 + (12ab + -16b2)) = 0
Reorder the terms:
(-12ab + 12ab + 9a2 + -16b2) = 0
Combine like terms: -12ab + 12ab = 0
(0 + 9a2 + -16b2) = 0
(9a2 + -16b2) = 0
Solving
9a2 + -16b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '16b2' to each side of the equation.
9a2 + -16b2 + 16b2 = 0 + 16b2
Combine like terms: -16b2 + 16b2 = 0
9a2 + 0 = 0 + 16b2
9a2 = 0 + 16b2
Remove the zero:
9a2 = 16b2
Divide each side by '9'.
a2 = 1.777777778b2
Simplifying
a2 = 1.777777778b2
Take the square root of each side:
a = {-1.333333333b, 1.333333333b}
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