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Simplifying
(2a + 2d)(2a + -2d) = 0
Multiply (2a + 2d) * (2a + -2d)
(2a * (2a + -2d) + 2d * (2a + -2d)) = 0
((2a * 2a + -2d * 2a) + 2d * (2a + -2d)) = 0
Reorder the terms:
((-4ad + 4a2) + 2d * (2a + -2d)) = 0
((-4ad + 4a2) + 2d * (2a + -2d)) = 0
(-4ad + 4a2 + (2a * 2d + -2d * 2d)) = 0
(-4ad + 4a2 + (4ad + -4d2)) = 0
Reorder the terms:
(-4ad + 4ad + 4a2 + -4d2) = 0
Combine like terms: -4ad + 4ad = 0
(0 + 4a2 + -4d2) = 0
(4a2 + -4d2) = 0
Solving
4a2 + -4d2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '4d2' to each side of the equation.
4a2 + -4d2 + 4d2 = 0 + 4d2
Combine like terms: -4d2 + 4d2 = 0
4a2 + 0 = 0 + 4d2
4a2 = 0 + 4d2
Remove the zero:
4a2 = 4d2
Divide each side by '4'.
a2 = d2
Simplifying
a2 = d2
Take the square root of each side:
a = {-1d, d}
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