4x^2+4x+1=169

Solution for 4x^2+4x+1=169 equation:

Simplifying
4x2 + 4x + 1 = 169

Reorder the terms:
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}