12a^2-13a=25

Solution for 12a^2-13a=25 equation:

Simplifying
12a2 + -13a = 25

Reorder the terms:
-13a + 12a2 = 25

Solving
-13a + 12a2 = 25

Solving for variable 'a'.

Reorder the terms:
-25 + -13a + 12a2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -13a + 12a2 = 0

Factor a trinomial.
(-1 + -1a)(25 + -12a) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 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 + -1a = 0 + 1

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(25 + -12a)' equal to zero and attempt to solve:

Simplifying
25 + -12a = 0

Solving
25 + -12a = 0

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

Add '-25' to each side of the equation.
25 + -25 + -12a = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -12a = 0 + -25
-12a = 0 + -25

Combine like terms: 0 + -25 = -25
-12a = -25

Divide each side by '-12'.
a = 2.083333333

Simplifying
a = 2.083333333
Solution
a = {-1, 2.083333333}