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Simplifying
2a(a + 1) + a2 = 2a + 12
Reorder the terms:
2a(1 + a) + a2 = 2a + 12
(1 * 2a + a * 2a) + a2 = 2a + 12
(2a + 2a2) + a2 = 2a + 12
Combine like terms: 2a2 + a2 = 3a2
2a + 3a2 = 2a + 12
Reorder the terms:
2a + 3a2 = 12 + 2a
Add '-2a' to each side of the equation.
2a + -2a + 3a2 = 12 + 2a + -2a
Combine like terms: 2a + -2a = 0
0 + 3a2 = 12 + 2a + -2a
3a2 = 12 + 2a + -2a
Combine like terms: 2a + -2a = 0
3a2 = 12 + 0
3a2 = 12
Solving
3a2 = 12
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Divide each side by '3'.
a2 = 4
Simplifying
a2 = 4
Take the square root of each side:
a = {-2, 2}
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