7ax+2x^2-60a^2=0

Solution for 7ax+2x^2-60a^2=0 equation:

Simplifying
7ax + 2x2 + -60a2 = 0

Reorder the terms:
7ax + -60a2 + 2x2 = 0

Solving
7ax + -60a2 + 2x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-15a + -2x)(4a + -1x) = 0

Subproblem 1
Set the factor '(-15a + -2x)' equal to zero and attempt to solve:

Simplifying
-15a + -2x = 0

Solving
-15a + -2x = 0

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

Add '2x' to each side of the equation.
-15a + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
-15a + 0 = 0 + 2x
-15a = 0 + 2x
Remove the zero:
-15a = 2x

Divide each side by '-15'.
a = -0.1333333333x

Simplifying
a = -0.1333333333x
Subproblem 2
Set the factor '(4a + -1x)' equal to zero and attempt to solve:

Simplifying
4a + -1x = 0

Solving
4a + -1x = 0

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

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

Combine like terms: -1x + x = 0
4a + 0 = 0 + x
4a = 0 + x
Remove the zero:
4a = x

Divide each side by '4'.
a = 0.25x

Simplifying
a = 0.25x
Solution
a = {-0.1333333333x, 0.25x}