(2x+1)(2x+1)=169

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Solution for (2x+1)(2x+1)=169 equation: 


Simplifying
(2x + 1)(2x + 1) = 169

Reorder the terms:
(1 + 2x)(2x + 1) = 169

Reorder the terms:
(1 + 2x)(1 + 2x) = 169

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) = 169
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 169
((1 + 2x) + 2x * (1 + 2x)) = 169
(1 + 2x + (1 * 2x + 2x * 2x)) = 169
(1 + 2x + (2x + 4x2)) = 169

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) = 169

Solving
1 + 4x + 4x2 = 169

Solving for variable 'x'.

Reorder the terms:
1 + -169 + 4x + 4x2 = 169 + -169

Combine like terms: 1 + -169 = -168
-168 + 4x + 4x2 = 169 + -169

Combine like terms: 169 + -169 = 0
-168 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 6}

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