8b^2-6=b(2b-5)

Solution for 8b^2-6=b(2b-5) equation:

Simplifying
8b2 + -6 = b(2b + -5)

Reorder the terms:
-6 + 8b2 = b(2b + -5)

Reorder the terms:
-6 + 8b2 = b(-5 + 2b)
-6 + 8b2 = (-5 * b + 2b * b)
-6 + 8b2 = (-5b + 2b2)

Solving
-6 + 8b2 = -5b + 2b2

Solving for variable 'b'.

Reorder the terms:
-6 + 5b + 8b2 + -2b2 = -5b + 2b2 + 5b + -2b2

Combine like terms: 8b2 + -2b2 = 6b2
-6 + 5b + 6b2 = -5b + 2b2 + 5b + -2b2

Reorder the terms:
-6 + 5b + 6b2 = -5b + 5b + 2b2 + -2b2

Combine like terms: -5b + 5b = 0
-6 + 5b + 6b2 = 0 + 2b2 + -2b2
-6 + 5b + 6b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
-6 + 5b + 6b2 = 0

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

Subproblem 1
Set the factor '(-3 + -2b)' equal to zero and attempt to solve:

Simplifying
-3 + -2b = 0

Solving
-3 + -2b = 0

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

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

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

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

Divide each side by '-2'.
b = -1.5

Simplifying
b = -1.5
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 = {-1.5, 0.6666666667}