(4x+1)(4x+1)=9

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Solution for (4x+1)(4x+1)=9 equation: 


Simplifying
(4x + 1)(4x + 1) = 9

Reorder the terms:
(1 + 4x)(4x + 1) = 9

Reorder the terms:
(1 + 4x)(1 + 4x) = 9

Multiply (1 + 4x) * (1 + 4x)
(1(1 + 4x) + 4x * (1 + 4x)) = 9
((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = 9
((1 + 4x) + 4x * (1 + 4x)) = 9
(1 + 4x + (1 * 4x + 4x * 4x)) = 9
(1 + 4x + (4x + 16x2)) = 9

Combine like terms: 4x + 4x = 8x
(1 + 8x + 16x2) = 9

Solving
1 + 8x + 16x2 = 9

Solving for variable 'x'.

Reorder the terms:
1 + -9 + 8x + 16x2 = 9 + -9

Combine like terms: 1 + -9 = -8
-8 + 8x + 16x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-8 + 8x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + x + 2x2) = 0

Factor a trinomial.
8((-1 + -1x)(1 + -2x)) = 0

Ignore the factor 8.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1, 0.5}

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