-2a^2-6a+15=7-3a^2

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Solution for -2a^2-6a+15=7-3a^2 equation: 


Simplifying
-2a2 + -6a + 15 = 7 + -3a2

Reorder the terms:
15 + -6a + -2a2 = 7 + -3a2

Solving
15 + -6a + -2a2 = 7 + -3a2

Solving for variable 'a'.

Reorder the terms:
15 + -7 + -6a + -2a2 + 3a2 = 7 + -3a2 + -7 + 3a2

Combine like terms: 15 + -7 = 8
8 + -6a + -2a2 + 3a2 = 7 + -3a2 + -7 + 3a2

Combine like terms: -2a2 + 3a2 = 1a2
8 + -6a + 1a2 = 7 + -3a2 + -7 + 3a2

Reorder the terms:
8 + -6a + 1a2 = 7 + -7 + -3a2 + 3a2

Combine like terms: 7 + -7 = 0
8 + -6a + 1a2 = 0 + -3a2 + 3a2
8 + -6a + 1a2 = -3a2 + 3a2

Combine like terms: -3a2 + 3a2 = 0
8 + -6a + 1a2 = 0

Factor a trinomial.
(2 + -1a)(4 + -1a) = 0


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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2

Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {2, 4}

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