42b^2=12-30b

Solution for 42b^2=12-30b equation:

Simplifying
42b2 = 12 + -30b

Solving
42b2 = 12 + -30b

Solving for variable 'b'.

Reorder the terms:
-12 + 30b + 42b2 = 12 + -30b + -12 + 30b

Reorder the terms:
-12 + 30b + 42b2 = 12 + -12 + -30b + 30b

Combine like terms: 12 + -12 = 0
-12 + 30b + 42b2 = 0 + -30b + 30b
-12 + 30b + 42b2 = -30b + 30b

Combine like terms: -30b + 30b = 0
-12 + 30b + 42b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 5b + 7b2) = 0

Factor a trinomial.
6((-1 + -1b)(2 + -7b)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -7b)' equal to zero and attempt to solve:

Simplifying
2 + -7b = 0

Solving
2 + -7b = 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 + -7b = 0 + -2

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

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

Divide each side by '-7'.
b = 0.2857142857

Simplifying
b = 0.2857142857
Solution
b = {-1, 0.2857142857}