0=2a^2+7a+3

Solution for 0=2a^2+7a+3 equation:

Simplifying
0 = 2a2 + 7a + 3

Reorder the terms:
0 = 3 + 7a + 2a2

Solving
0 = 3 + 7a + 2a2

Solving for variable 'a'.

Combine like terms: 0 + -3 = -3
-3 + -7a + -2a2 = 3 + 7a + 2a2 + -3 + -7a + -2a2

Reorder the terms:
-3 + -7a + -2a2 = 3 + -3 + 7a + -7a + 2a2 + -2a2

Combine like terms: 3 + -3 = 0
-3 + -7a + -2a2 = 0 + 7a + -7a + 2a2 + -2a2
-3 + -7a + -2a2 = 7a + -7a + 2a2 + -2a2

Combine like terms: 7a + -7a = 0
-3 + -7a + -2a2 = 0 + 2a2 + -2a2
-3 + -7a + -2a2 = 2a2 + -2a2

Combine like terms: 2a2 + -2a2 = 0
-3 + -7a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7a + 2a2) = 0

Factor a trinomial.
-1((3 + a)(1 + 2a)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(1 + 2a)' equal to zero and attempt to solve:

Simplifying
1 + 2a = 0

Solving
1 + 2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-3, -0.5}