0=30a^2b+7ab-49b

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Solution for 0=30a^2b+7ab-49b equation: 


Simplifying
0 = 30a2b + 7ab + -49b

Reorder the terms:
0 = 7ab + 30a2b + -49b

Solving
0 = 7ab + 30a2b + -49b

Solving for variable 'a'.
Remove the zero:
-7ab + -30a2b + 49b = 7ab + 30a2b + -49b + -7ab + -30a2b + 49b

Reorder the terms:
-7ab + -30a2b + 49b = 7ab + -7ab + 30a2b + -30a2b + -49b + 49b

Combine like terms: 7ab + -7ab = 0
-7ab + -30a2b + 49b = 0 + 30a2b + -30a2b + -49b + 49b
-7ab + -30a2b + 49b = 30a2b + -30a2b + -49b + 49b

Combine like terms: 30a2b + -30a2b = 0
-7ab + -30a2b + 49b = 0 + -49b + 49b
-7ab + -30a2b + 49b = -49b + 49b

Combine like terms: -49b + 49b = 0
-7ab + -30a2b + 49b = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(-7a + -30a2 + 49) = 0

Factor a trinomial.
b((-5a + -7)(6a + -7)) = 0


Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-5a + -7)' equal to zero and attempt to solve:

Simplifying
-5a + -7 = 0

Reorder the terms:
-7 + -5a = 0

Solving
-7 + -5a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5a = 0 + 7
-5a = 0 + 7

Combine like terms: 0 + 7 = 7
-5a = 7

Divide each side by '-5'.
a = -1.4

Simplifying
a = -1.4

Subproblem 3
Set the factor '(6a + -7)' equal to zero and attempt to solve:

Simplifying
6a + -7 = 0

Reorder the terms:
-7 + 6a = 0

Solving
-7 + 6a = 0

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

Add '7' to each side of the equation.
-7 + 7 + 6a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 6a = 0 + 7
6a = 0 + 7

Combine like terms: 0 + 7 = 7
6a = 7

Divide each side by '6'.
a = 1.166666667

Simplifying
a = 1.166666667
Solution
a = {-1.4, 1.166666667}

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