2a(a+2)-2a*2+1=19

Solution for 2a(a+2)-2a*2+1=19 equation:

Simplifying
2a(a + 2) + -2a * 2 + 1 = 19

Reorder the terms:
2a(2 + a) + -2a * 2 + 1 = 19
(2 * 2a + a * 2a) + -2a * 2 + 1 = 19
(4a + 2a2) + -2a * 2 + 1 = 19

Reorder the terms for easier multiplication:
4a + 2a2 + -2 * 2a + 1 = 19

Multiply -2 * 2
4a + 2a2 + -4a + 1 = 19

Reorder the terms:
1 + 4a + -4a + 2a2 = 19

Combine like terms: 4a + -4a = 0
1 + 0 + 2a2 = 19
1 + 2a2 = 19

Solving
1 + 2a2 = 19

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2a2 = 19 + -1

Combine like terms: 1 + -1 = 0
0 + 2a2 = 19 + -1
2a2 = 19 + -1

Combine like terms: 19 + -1 = 18
2a2 = 18

Divide each side by '2'.
a2 = 9

Simplifying
a2 = 9

Take the square root of each side:
a = {-3, 3}