3b^2-5b-3=-6b+1

Solution for 3b^2-5b-3=-6b+1 equation:

Simplifying
3b2 + -5b + -3 = -6b + 1

Reorder the terms:
-3 + -5b + 3b2 = -6b + 1

Reorder the terms:
-3 + -5b + 3b2 = 1 + -6b

Solving
-3 + -5b + 3b2 = 1 + -6b

Solving for variable 'b'.

Reorder the terms:
-3 + -1 + -5b + 6b + 3b2 = 1 + -6b + -1 + 6b

Combine like terms: -3 + -1 = -4
-4 + -5b + 6b + 3b2 = 1 + -6b + -1 + 6b

Combine like terms: -5b + 6b = 1b
-4 + 1b + 3b2 = 1 + -6b + -1 + 6b

Reorder the terms:
-4 + 1b + 3b2 = 1 + -1 + -6b + 6b

Combine like terms: 1 + -1 = 0
-4 + 1b + 3b2 = 0 + -6b + 6b
-4 + 1b + 3b2 = -6b + 6b

Combine like terms: -6b + 6b = 0
-4 + 1b + 3b2 = 0

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

Subproblem 1
Set the factor '(-4 + -3b)' equal to zero and attempt to solve:

Simplifying
-4 + -3b = 0

Solving
-4 + -3b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3b = 0 + 4
-3b = 0 + 4

Combine like terms: 0 + 4 = 4
-3b = 4

Divide each side by '-3'.
b = -1.333333333

Simplifying
b = -1.333333333
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1b = 0 + -1
-1b = 0 + -1

Combine like terms: 0 + -1 = -1
-1b = -1

Divide each side by '-1'.
b = 1

Simplifying
b = 1
Solution
b = {-1.333333333, 1}