4b^2-6+10b=0

Solution for 4b^2-6+10b=0 equation:

Simplifying
4b2 + -6 + 10b = 0

Reorder the terms:
-6 + 10b + 4b2 = 0

Solving
-6 + 10b + 4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5b + 2b2) = 0

Factor a trinomial.
2((-3 + -1b)(1 + -2b)) = 0

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

Simplifying
-3 + -1b = 0

Solving
-3 + -1b = 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 + -1b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1b = 0 + 3
-1b = 0 + 3

Combine like terms: 0 + 3 = 3
-1b = 3

Divide each side by '-1'.
b = -3

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

Simplifying
1 + -2b = 0

Solving
1 + -2b = 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 + -2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2b = 0 + -1
-2b = 0 + -1

Combine like terms: 0 + -1 = -1
-2b = -1

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Solution
b = {-3, 0.5}