4a^2-12a-(a-3)=0

Solution for 4a^2-12a-(a-3)=0 equation:

Simplifying
4a2 + -12a + -1(a + -3) = 0

Reorder the terms:
4a2 + -12a + -1(-3 + a) = 0
4a2 + -12a + (-3 * -1 + a * -1) = 0
4a2 + -12a + (3 + -1a) = 0

Reorder the terms:
3 + -12a + -1a + 4a2 = 0

Combine like terms: -12a + -1a = -13a
3 + -13a + 4a2 = 0

Solving
3 + -13a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -4a)(3 + -1a) = 0

Subproblem 1
Set the factor '(1 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4a = 0 + -1
-4a = 0 + -1

Combine like terms: 0 + -1 = -1
-4a = -1

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {0.25, 3}