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Simplifying
2a(5a + 10) + (2a + -8)(3a + 2) = 0
Reorder the terms:
2a(10 + 5a) + (2a + -8)(3a + 2) = 0
(10 * 2a + 5a * 2a) + (2a + -8)(3a + 2) = 0
(20a + 10a2) + (2a + -8)(3a + 2) = 0
Reorder the terms:
20a + 10a2 + (-8 + 2a)(3a + 2) = 0
Reorder the terms:
20a + 10a2 + (-8 + 2a)(2 + 3a) = 0
Multiply (-8 + 2a) * (2 + 3a)
20a + 10a2 + (-8(2 + 3a) + 2a * (2 + 3a)) = 0
20a + 10a2 + ((2 * -8 + 3a * -8) + 2a * (2 + 3a)) = 0
20a + 10a2 + ((-16 + -24a) + 2a * (2 + 3a)) = 0
20a + 10a2 + (-16 + -24a + (2 * 2a + 3a * 2a)) = 0
20a + 10a2 + (-16 + -24a + (4a + 6a2)) = 0
Combine like terms: -24a + 4a = -20a
20a + 10a2 + (-16 + -20a + 6a2) = 0
Reorder the terms:
-16 + 20a + -20a + 10a2 + 6a2 = 0
Combine like terms: 20a + -20a = 0
-16 + 0 + 10a2 + 6a2 = 0
-16 + 10a2 + 6a2 = 0
Combine like terms: 10a2 + 6a2 = 16a2
-16 + 16a2 = 0
Solving
-16 + 16a2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '16' to each side of the equation.
-16 + 16 + 16a2 = 0 + 16
Combine like terms: -16 + 16 = 0
0 + 16a2 = 0 + 16
16a2 = 0 + 16
Combine like terms: 0 + 16 = 16
16a2 = 16
Divide each side by '16'.
a2 = 1
Simplifying
a2 = 1
Take the square root of each side:
a = {-1, 1}
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