3x^2=a^2-2ax

Solution for 3x^2=a^2-2ax equation:

Simplifying
3x2 = a2 + -2ax

Reorder the terms:
3x2 = -2ax + a2

Solving
3x2 = -2ax + a2

Solving for variable 'x'.

Reorder the terms:
2ax + -1a2 + 3x2 = -2ax + a2 + 2ax + -1a2

Reorder the terms:
2ax + -1a2 + 3x2 = -2ax + 2ax + a2 + -1a2

Combine like terms: -2ax + 2ax = 0
2ax + -1a2 + 3x2 = 0 + a2 + -1a2
2ax + -1a2 + 3x2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
2ax + -1a2 + 3x2 = 0

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

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

Simplifying
-1a + -1x = 0

Solving
-1a + -1x = 0

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

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

Combine like terms: -1a + a = 0
0 + -1x = 0 + a
-1x = 0 + a
Remove the zero:
-1x = a

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

Simplifying
x = -1a
Subproblem 2
Set the factor '(a + -3x)' equal to zero and attempt to solve:

Simplifying
a + -3x = 0

Solving
a + -3x = 0

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

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

Combine like terms: a + -1a = 0
0 + -3x = 0 + -1a
-3x = 0 + -1a
Remove the zero:
-3x = -1a

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

Simplifying
x = 0.3333333333a
Solution
x = {-1a, 0.3333333333a}