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Simplifying
(7c + 3g)(7c + -3g) = 0
Multiply (7c + 3g) * (7c + -3g)
(7c * (7c + -3g) + 3g * (7c + -3g)) = 0
((7c * 7c + -3g * 7c) + 3g * (7c + -3g)) = 0
Reorder the terms:
((-21cg + 49c2) + 3g * (7c + -3g)) = 0
((-21cg + 49c2) + 3g * (7c + -3g)) = 0
(-21cg + 49c2 + (7c * 3g + -3g * 3g)) = 0
(-21cg + 49c2 + (21cg + -9g2)) = 0
Reorder the terms:
(-21cg + 21cg + 49c2 + -9g2) = 0
Combine like terms: -21cg + 21cg = 0
(0 + 49c2 + -9g2) = 0
(49c2 + -9g2) = 0
Solving
49c2 + -9g2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '9g2' to each side of the equation.
49c2 + -9g2 + 9g2 = 0 + 9g2
Combine like terms: -9g2 + 9g2 = 0
49c2 + 0 = 0 + 9g2
49c2 = 0 + 9g2
Remove the zero:
49c2 = 9g2
Divide each side by '49'.
c2 = 0.1836734694g2
Simplifying
c2 = 0.1836734694g2
Take the square root of each side:
c = {-0.428571429g, 0.428571429g}
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