(2x-1)(2x-1)=49

Solution for (2x-1)(2x-1)=49 equation:

Simplifying
(2x + -1)(2x + -1) = 49

Reorder the terms:
(-1 + 2x)(2x + -1) = 49

Reorder the terms:
(-1 + 2x)(-1 + 2x) = 49

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) = 49
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 49
((1 + -2x) + 2x * (-1 + 2x)) = 49
(1 + -2x + (-1 * 2x + 2x * 2x)) = 49
(1 + -2x + (-2x + 4x2)) = 49

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) = 49

Solving
1 + -4x + 4x2 = 49

Solving for variable 'x'.

Reorder the terms:
1 + -49 + -4x + 4x2 = 49 + -49

Combine like terms: 1 + -49 = -48
-48 + -4x + 4x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-48 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -1x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(4 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

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

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}