2a^2-a+4=14a-14

Solution for 2a^2-a+4=14a-14 equation:

Simplifying
2a2 + -1a + 4 = 14a + -14

Reorder the terms:
4 + -1a + 2a2 = 14a + -14

Reorder the terms:
4 + -1a + 2a2 = -14 + 14a

Solving
4 + -1a + 2a2 = -14 + 14a

Solving for variable 'a'.

Reorder the terms:
4 + 14 + -1a + -14a + 2a2 = -14 + 14a + 14 + -14a

Combine like terms: 4 + 14 = 18
18 + -1a + -14a + 2a2 = -14 + 14a + 14 + -14a

Combine like terms: -1a + -14a = -15a
18 + -15a + 2a2 = -14 + 14a + 14 + -14a

Reorder the terms:
18 + -15a + 2a2 = -14 + 14 + 14a + -14a

Combine like terms: -14 + 14 = 0
18 + -15a + 2a2 = 0 + 14a + -14a
18 + -15a + 2a2 = 14a + -14a

Combine like terms: 14a + -14a = 0
18 + -15a + 2a2 = 0

Factor a trinomial.
(3 + -2a)(6 + -1a) = 0

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

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

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

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

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {1.5, 6}