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Simplifying
(3ab + 10c2)(3ab + -10c2) = 0
Multiply (3ab + 10c2) * (3ab + -10c2)
(3ab * (3ab + -10c2) + 10c2 * (3ab + -10c2)) = 0
((3ab * 3ab + -10c2 * 3ab) + 10c2 * (3ab + -10c2)) = 0
Reorder the terms:
((-30abc2 + 9a2b2) + 10c2 * (3ab + -10c2)) = 0
((-30abc2 + 9a2b2) + 10c2 * (3ab + -10c2)) = 0
(-30abc2 + 9a2b2 + (3ab * 10c2 + -10c2 * 10c2)) = 0
(-30abc2 + 9a2b2 + (30abc2 + -100c4)) = 0
Reorder the terms:
(-30abc2 + 30abc2 + 9a2b2 + -100c4) = 0
Combine like terms: -30abc2 + 30abc2 = 0
(0 + 9a2b2 + -100c4) = 0
(9a2b2 + -100c4) = 0
Solving
9a2b2 + -100c4 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '100c4' to each side of the equation.
9a2b2 + -100c4 + 100c4 = 0 + 100c4
Combine like terms: -100c4 + 100c4 = 0
9a2b2 + 0 = 0 + 100c4
9a2b2 = 0 + 100c4
Remove the zero:
9a2b2 = 100c4
Divide each side by '9b2'.
a2 = 11.11111111b-2c4
Simplifying
a2 = 11.11111111b-2c4
Take the square root of each side:
a = {-3.333333333b-1c2, 3.333333333b-1c2}
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