10b^2-5b=30

Solution for 10b^2-5b=30 equation:

Simplifying
10b2 + -5b = 30

Reorder the terms:
-5b + 10b2 = 30

Solving
-5b + 10b2 = 30

Solving for variable 'b'.

Reorder the terms:
-30 + -5b + 10b2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -5b + 10b2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -1b + 2b2) = 0

Factor a trinomial.
5((-3 + -2b)(2 + -1b)) = 0

Ignore the factor 5.
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 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

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

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

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

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-1.5, 2}