(7x-3)(7x-3)=30

Solution for (7x-3)(7x-3)=30 equation:

Simplifying
(7x + -3)(7x + -3) = 30

Reorder the terms:
(-3 + 7x)(7x + -3) = 30

Reorder the terms:
(-3 + 7x)(-3 + 7x) = 30

Multiply (-3 + 7x) * (-3 + 7x)
(-3(-3 + 7x) + 7x * (-3 + 7x)) = 30
((-3 * -3 + 7x * -3) + 7x * (-3 + 7x)) = 30
((9 + -21x) + 7x * (-3 + 7x)) = 30
(9 + -21x + (-3 * 7x + 7x * 7x)) = 30
(9 + -21x + (-21x + 49x2)) = 30

Combine like terms: -21x + -21x = -42x
(9 + -42x + 49x2) = 30

Solving
9 + -42x + 49x2 = 30

Solving for variable 'x'.

Reorder the terms:
9 + -30 + -42x + 49x2 = 30 + -30

Combine like terms: 9 + -30 = -21
-21 + -42x + 49x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-21 + -42x + 49x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + -6x + 7x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + -6x + 7x2)' equal to zero and attempt to solve:

Simplifying
-3 + -6x + 7x2 = 0

Solving
-3 + -6x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-0.4285714286 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -0.8571428571x + 0.4285714286 + x2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -0.8571428571x + x2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -0.8571428571x + x2 = 0 + 0.4285714286
-0.8571428571x + x2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-0.8571428571x + x2 = 0.4285714286

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 0.4285714286 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 0.4285714286 + 0.1836734694

Combine like terms: 0.4285714286 + 0.1836734694 = 0.612244898
0.1836734694 + -0.8571428571x + x2 = 0.612244898

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 0.612244898

Calculate the square root of the right side: 0.782460796

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 0.782460796 and -0.782460796.

Subproblem 1
x + -0.4285714286 = 0.782460796

Simplifying
x + -0.4285714286 = 0.782460796

Reorder the terms:
-0.4285714286 + x = 0.782460796

Solving
-0.4285714286 + x = 0.782460796

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = 0.782460796 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = 0.782460796 + 0.4285714286
x = 0.782460796 + 0.4285714286

Combine like terms: 0.782460796 + 0.4285714286 = 1.2110322246
x = 1.2110322246

Simplifying
x = 1.2110322246

Subproblem 2
x + -0.4285714286 = -0.782460796

Simplifying
x + -0.4285714286 = -0.782460796

Reorder the terms:
-0.4285714286 + x = -0.782460796

Solving
-0.4285714286 + x = -0.782460796

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = -0.782460796 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = -0.782460796 + 0.4285714286
x = -0.782460796 + 0.4285714286

Combine like terms: -0.782460796 + 0.4285714286 = -0.3538893674
x = -0.3538893674

Simplifying
x = -0.3538893674

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2110322246, -0.3538893674}
Solution
x = {1.2110322246, -0.3538893674}