(2x-5)(2x-5)=49

Solution for (2x-5)(2x-5)=49 equation:

Simplifying
(2x + -5)(2x + -5) = 49

Reorder the terms:
(-5 + 2x)(2x + -5) = 49

Reorder the terms:
(-5 + 2x)(-5 + 2x) = 49

Multiply (-5 + 2x) * (-5 + 2x)
(-5(-5 + 2x) + 2x * (-5 + 2x)) = 49
((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 49
((25 + -10x) + 2x * (-5 + 2x)) = 49
(25 + -10x + (-5 * 2x + 2x * 2x)) = 49
(25 + -10x + (-10x + 4x2)) = 49

Combine like terms: -10x + -10x = -20x
(25 + -20x + 4x2) = 49

Solving
25 + -20x + 4x2 = 49

Solving for variable 'x'.

Reorder the terms:
25 + -49 + -20x + 4x2 = 49 + -49

Combine like terms: 25 + -49 = -24
-24 + -20x + 4x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-24 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -5x + x2) = 0

Factor a trinomial.
4((-1 + -1x)(6 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}