(3a-2)(4a+1)=5

Solution for (3a-2)(4a+1)=5 equation:

Simplifying
(3a + -2)(4a + 1) = 5

Reorder the terms:
(-2 + 3a)(4a + 1) = 5

Reorder the terms:
(-2 + 3a)(1 + 4a) = 5

Multiply (-2 + 3a) * (1 + 4a)
(-2(1 + 4a) + 3a * (1 + 4a)) = 5
((1 * -2 + 4a * -2) + 3a * (1 + 4a)) = 5
((-2 + -8a) + 3a * (1 + 4a)) = 5
(-2 + -8a + (1 * 3a + 4a * 3a)) = 5
(-2 + -8a + (3a + 12a2)) = 5

Combine like terms: -8a + 3a = -5a
(-2 + -5a + 12a2) = 5

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

Solving for variable 'a'.

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

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

Combine like terms: 5 + -5 = 0
-7 + -5a + 12a2 = 0

Factor a trinomial.
(-7 + -12a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -12a)' equal to zero and attempt to solve:

Simplifying
-7 + -12a = 0

Solving
-7 + -12a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -12a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12a = 0 + 7
-12a = 0 + 7

Combine like terms: 0 + 7 = 7
-12a = 7

Divide each side by '-12'.
a = -0.5833333333

Simplifying
a = -0.5833333333
Subproblem 2
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
Solution
a = {-0.5833333333, 1}