(5b-3)(3b+1)=1

Solution for (5b-3)(3b+1)=1 equation:

Simplifying
(5b + -3)(3b + 1) = 1

Reorder the terms:
(-3 + 5b)(3b + 1) = 1

Reorder the terms:
(-3 + 5b)(1 + 3b) = 1

Multiply (-3 + 5b) * (1 + 3b)
(-3(1 + 3b) + 5b * (1 + 3b)) = 1
((1 * -3 + 3b * -3) + 5b * (1 + 3b)) = 1
((-3 + -9b) + 5b * (1 + 3b)) = 1
(-3 + -9b + (1 * 5b + 3b * 5b)) = 1
(-3 + -9b + (5b + 15b2)) = 1

Combine like terms: -9b + 5b = -4b
(-3 + -4b + 15b2) = 1

Solving
-3 + -4b + 15b2 = 1

Solving for variable 'b'.

Reorder the terms:
-3 + -1 + -4b + 15b2 = 1 + -1

Combine like terms: -3 + -1 = -4
-4 + -4b + 15b2 = 1 + -1

Combine like terms: 1 + -1 = 0
-4 + -4b + 15b2 = 0

Factor a trinomial.
(-2 + -5b)(2 + -3b) = 0

Subproblem 1
Set the factor '(-2 + -5b)' equal to zero and attempt to solve:

Simplifying
-2 + -5b = 0

Solving
-2 + -5b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5b = 0 + 2
-5b = 0 + 2

Combine like terms: 0 + 2 = 2
-5b = 2

Divide each side by '-5'.
b = -0.4

Simplifying
b = -0.4
Subproblem 2
Set the factor '(2 + -3b)' equal to zero and attempt to solve:

Simplifying
2 + -3b = 0

Solving
2 + -3b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3b = 0 + -2
-3b = 0 + -2

Combine like terms: 0 + -2 = -2
-3b = -2

Divide each side by '-3'.
b = 0.6666666667

Simplifying
b = 0.6666666667
Solution
b = {-0.4, 0.6666666667}