a^2+7a-1=-a^2+14

Solution for a^2+7a-1=-a^2+14 equation:

Simplifying
a2 + 7a + -1 = -1a2 + 14

Reorder the terms:
-1 + 7a + a2 = -1a2 + 14

Reorder the terms:
-1 + 7a + a2 = 14 + -1a2

Solving
-1 + 7a + a2 = 14 + -1a2

Solving for variable 'a'.

Reorder the terms:
-1 + -14 + 7a + a2 + a2 = 14 + -1a2 + -14 + a2

Combine like terms: -1 + -14 = -15
-15 + 7a + a2 + a2 = 14 + -1a2 + -14 + a2

Combine like terms: a2 + a2 = 2a2
-15 + 7a + 2a2 = 14 + -1a2 + -14 + a2

Reorder the terms:
-15 + 7a + 2a2 = 14 + -14 + -1a2 + a2

Combine like terms: 14 + -14 = 0
-15 + 7a + 2a2 = 0 + -1a2 + a2
-15 + 7a + 2a2 = -1a2 + a2

Combine like terms: -1a2 + a2 = 0
-15 + 7a + 2a2 = 0

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

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1a = 0 + 5
-1a = 0 + 5

Combine like terms: 0 + 5 = 5
-1a = 5

Divide each side by '-1'.
a = -5

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

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-5, 1.5}