3a^2+2=7a

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

Simplifying
3a2 + 2 = 7a

Reorder the terms:
2 + 3a2 = 7a

Solving
2 + 3a2 = 7a

Solving for variable 'a'.

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

Combine like terms: 7a + -7a = 0
2 + -7a + 3a2 = 0

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

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

Simplifying
1 + -3a = 0

Solving
1 + -3a = 0

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

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

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

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

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
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 = {0.3333333333, 2}