(4x+2)(4x+2)=196

Solution for (4x+2)(4x+2)=196 equation:

Simplifying
(4x + 2)(4x + 2) = 196

Reorder the terms:
(2 + 4x)(4x + 2) = 196

Reorder the terms:
(2 + 4x)(2 + 4x) = 196

Multiply (2 + 4x) * (2 + 4x)
(2(2 + 4x) + 4x * (2 + 4x)) = 196
((2 * 2 + 4x * 2) + 4x * (2 + 4x)) = 196
((4 + 8x) + 4x * (2 + 4x)) = 196
(4 + 8x + (2 * 4x + 4x * 4x)) = 196
(4 + 8x + (8x + 16x2)) = 196

Combine like terms: 8x + 8x = 16x
(4 + 16x + 16x2) = 196

Solving
4 + 16x + 16x2 = 196

Solving for variable 'x'.

Reorder the terms:
4 + -196 + 16x + 16x2 = 196 + -196

Combine like terms: 4 + -196 = -192
-192 + 16x + 16x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-192 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-12 + x + x2) = 0

Factor a trinomial.
16((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 16.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-4, 3}