-161+91a=7-49a^2

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Solution for -161+91a=7-49a^2 equation: 


Simplifying
-161 + 91a = 7 + -49a2

Solving
-161 + 91a = 7 + -49a2

Solving for variable 'a'.

Reorder the terms:
-161 + -7 + 91a + 49a2 = 7 + -49a2 + -7 + 49a2

Combine like terms: -161 + -7 = -168
-168 + 91a + 49a2 = 7 + -49a2 + -7 + 49a2

Reorder the terms:
-168 + 91a + 49a2 = 7 + -7 + -49a2 + 49a2

Combine like terms: 7 + -7 = 0
-168 + 91a + 49a2 = 0 + -49a2 + 49a2
-168 + 91a + 49a2 = -49a2 + 49a2

Combine like terms: -49a2 + 49a2 = 0
-168 + 91a + 49a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-24 + 13a + 7a2) = 0

Factor a trinomial.
7((-3 + -1a)(8 + -7a)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

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

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

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

Simplifying
a = -3

Subproblem 2
Set the factor '(8 + -7a)' equal to zero and attempt to solve:

Simplifying
8 + -7a = 0

Solving
8 + -7a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7a = 0 + -8
-7a = 0 + -8

Combine like terms: 0 + -8 = -8
-7a = -8

Divide each side by '-7'.
a = 1.142857143

Simplifying
a = 1.142857143
Solution
a = {-3, 1.142857143}

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