2a^2+3a=14

Solution for 2a^2+3a=14 equation:

Simplifying
2a2 + 3a = 14

Reorder the terms:
3a + 2a2 = 14

Solving
3a + 2a2 = 14

Solving for variable 'a'.

Reorder the terms:
-14 + 3a + 2a2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 3a + 2a2 = 0

Factor a trinomial.
(-7 + -2a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve:

Simplifying
-7 + -2a = 0

Solving
-7 + -2a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2a = 0 + 7

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

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

Divide each side by '-2'.
a = -3.5

Simplifying
a = -3.5
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-3.5, 2}