(4a-1)(a-1)=10

Solution for (4a-1)(a-1)=10 equation:

Simplifying
(4a + -1)(a + -1) = 10

Reorder the terms:
(-1 + 4a)(a + -1) = 10

Reorder the terms:
(-1 + 4a)(-1 + a) = 10

Multiply (-1 + 4a) * (-1 + a)
(-1(-1 + a) + 4a * (-1 + a)) = 10
((-1 * -1 + a * -1) + 4a * (-1 + a)) = 10
((1 + -1a) + 4a * (-1 + a)) = 10
(1 + -1a + (-1 * 4a + a * 4a)) = 10
(1 + -1a + (-4a + 4a2)) = 10

Combine like terms: -1a + -4a = -5a
(1 + -5a + 4a2) = 10

Solving
1 + -5a + 4a2 = 10

Solving for variable 'a'.

Reorder the terms:
1 + -10 + -5a + 4a2 = 10 + -10

Combine like terms: 1 + -10 = -9
-9 + -5a + 4a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9 + -5a + 4a2 = 0

Factor a trinomial.
(-1 + -1a)(9 + -4a) = 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 '(9 + -4a)' equal to zero and attempt to solve:

Simplifying
9 + -4a = 0

Solving
9 + -4a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4a = 0 + -9
-4a = 0 + -9

Combine like terms: 0 + -9 = -9
-4a = -9

Divide each side by '-4'.
a = 2.25

Simplifying
a = 2.25
Solution
a = {-1, 2.25}