6a^2+5a=12a-2

Solution for 6a^2+5a=12a-2 equation:

Simplifying
6a2 + 5a = 12a + -2

Reorder the terms:
5a + 6a2 = 12a + -2

Reorder the terms:
5a + 6a2 = -2 + 12a

Solving
5a + 6a2 = -2 + 12a

Solving for variable 'a'.

Reorder the terms:
2 + 5a + -12a + 6a2 = -2 + 12a + 2 + -12a

Combine like terms: 5a + -12a = -7a
2 + -7a + 6a2 = -2 + 12a + 2 + -12a

Reorder the terms:
2 + -7a + 6a2 = -2 + 2 + 12a + -12a

Combine like terms: -2 + 2 = 0
2 + -7a + 6a2 = 0 + 12a + -12a
2 + -7a + 6a2 = 12a + -12a

Combine like terms: 12a + -12a = 0
2 + -7a + 6a2 = 0

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

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

Simplifying
2 + -3a = 0

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

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

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

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {0.5, 0.6666666667}