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Simplifying
(4a + 3g)(4a + -3g) = 0
Multiply (4a + 3g) * (4a + -3g)
(4a * (4a + -3g) + 3g * (4a + -3g)) = 0
((4a * 4a + -3g * 4a) + 3g * (4a + -3g)) = 0
Reorder the terms:
((-12ag + 16a2) + 3g * (4a + -3g)) = 0
((-12ag + 16a2) + 3g * (4a + -3g)) = 0
(-12ag + 16a2 + (4a * 3g + -3g * 3g)) = 0
(-12ag + 16a2 + (12ag + -9g2)) = 0
Reorder the terms:
(-12ag + 12ag + 16a2 + -9g2) = 0
Combine like terms: -12ag + 12ag = 0
(0 + 16a2 + -9g2) = 0
(16a2 + -9g2) = 0
Solving
16a2 + -9g2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9g2' to each side of the equation.
16a2 + -9g2 + 9g2 = 0 + 9g2
Combine like terms: -9g2 + 9g2 = 0
16a2 + 0 = 0 + 9g2
16a2 = 0 + 9g2
Remove the zero:
16a2 = 9g2
Divide each side by '16'.
a2 = 0.5625g2
Simplifying
a2 = 0.5625g2
Take the square root of each side:
a = {-0.75g, 0.75g}
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