(2a-1)(a-6)=6

Solution for (2a-1)(a-6)=6 equation:

Simplifying
(2a + -1)(a + -6) = 6

Reorder the terms:
(-1 + 2a)(a + -6) = 6

Reorder the terms:
(-1 + 2a)(-6 + a) = 6

Multiply (-1 + 2a) * (-6 + a)
(-1(-6 + a) + 2a * (-6 + a)) = 6
((-6 * -1 + a * -1) + 2a * (-6 + a)) = 6
((6 + -1a) + 2a * (-6 + a)) = 6
(6 + -1a + (-6 * 2a + a * 2a)) = 6
(6 + -1a + (-12a + 2a2)) = 6

Combine like terms: -1a + -12a = -13a
(6 + -13a + 2a2) = 6

Add '-6' to each side of the equation.
6 + -13a + -6 + 2a2 = 6 + -6

Reorder the terms:
6 + -6 + -13a + 2a2 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + -13a + 2a2 = 6 + -6
-13a + 2a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-13a + 2a2 = 0

Solving
-13a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-13 + 2a) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-13 + 2a)' equal to zero and attempt to solve:

Simplifying
-13 + 2a = 0

Solving
-13 + 2a = 0

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

Add '13' to each side of the equation.
-13 + 13 + 2a = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 2a = 0 + 13
2a = 0 + 13

Combine like terms: 0 + 13 = 13
2a = 13

Divide each side by '2'.
a = 6.5

Simplifying
a = 6.5
Solution
a = {0, 6.5}