6b^2+21b=10b+35

Solution for 6b^2+21b=10b+35 equation:

Simplifying
6b2 + 21b = 10b + 35

Reorder the terms:
21b + 6b2 = 10b + 35

Reorder the terms:
21b + 6b2 = 35 + 10b

Solving
21b + 6b2 = 35 + 10b

Solving for variable 'b'.

Reorder the terms:
-35 + 21b + -10b + 6b2 = 35 + 10b + -35 + -10b

Combine like terms: 21b + -10b = 11b
-35 + 11b + 6b2 = 35 + 10b + -35 + -10b

Reorder the terms:
-35 + 11b + 6b2 = 35 + -35 + 10b + -10b

Combine like terms: 35 + -35 = 0
-35 + 11b + 6b2 = 0 + 10b + -10b
-35 + 11b + 6b2 = 10b + -10b

Combine like terms: 10b + -10b = 0
-35 + 11b + 6b2 = 0

Factor a trinomial.
(-7 + -2b)(5 + -3b) = 0

Subproblem 1
Set the factor '(-7 + -2b)' equal to zero and attempt to solve:

Simplifying
-7 + -2b = 0

Solving
-7 + -2b = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2b = 0 + 7
-2b = 0 + 7

Combine like terms: 0 + 7 = 7
-2b = 7

Divide each side by '-2'.
b = -3.5

Simplifying
b = -3.5
Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve:

Simplifying
5 + -3b = 0

Solving
5 + -3b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3b = 0 + -5
-3b = 0 + -5

Combine like terms: 0 + -5 = -5
-3b = -5

Divide each side by '-3'.
b = 1.666666667

Simplifying
b = 1.666666667
Solution
b = {-3.5, 1.666666667}