2(a^2+3)=7a

Solution for 2(a^2+3)=7a equation:

Simplifying
2(a2 + 3) = 7a

Reorder the terms:
2(3 + a2) = 7a
(3 * 2 + a2 * 2) = 7a
(6 + 2a2) = 7a

Solving
6 + 2a2 = 7a

Solving for variable 'a'.

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

Combine like terms: 7a + -7a = 0
6 + -7a + 2a2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {1.5, 2}