(4x+1)(4x+1)=(3x-1)(3x-1)

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Solution for (4x+1)(4x+1)=(3x-1)(3x-1) equation: 


Simplifying
(4x + 1)(4x + 1) = (3x + -1)(3x + -1)

Reorder the terms:
(1 + 4x)(4x + 1) = (3x + -1)(3x + -1)

Reorder the terms:
(1 + 4x)(1 + 4x) = (3x + -1)(3x + -1)

Multiply (1 + 4x) * (1 + 4x)
(1(1 + 4x) + 4x * (1 + 4x)) = (3x + -1)(3x + -1)
((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = (3x + -1)(3x + -1)
((1 + 4x) + 4x * (1 + 4x)) = (3x + -1)(3x + -1)
(1 + 4x + (1 * 4x + 4x * 4x)) = (3x + -1)(3x + -1)
(1 + 4x + (4x + 16x2)) = (3x + -1)(3x + -1)

Combine like terms: 4x + 4x = 8x
(1 + 8x + 16x2) = (3x + -1)(3x + -1)

Reorder the terms:
1 + 8x + 16x2 = (-1 + 3x)(3x + -1)

Reorder the terms:
1 + 8x + 16x2 = (-1 + 3x)(-1 + 3x)

Multiply (-1 + 3x) * (-1 + 3x)
1 + 8x + 16x2 = (-1(-1 + 3x) + 3x * (-1 + 3x))
1 + 8x + 16x2 = ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x))
1 + 8x + 16x2 = ((1 + -3x) + 3x * (-1 + 3x))
1 + 8x + 16x2 = (1 + -3x + (-1 * 3x + 3x * 3x))
1 + 8x + 16x2 = (1 + -3x + (-3x + 9x2))

Combine like terms: -3x + -3x = -6x
1 + 8x + 16x2 = (1 + -6x + 9x2)

Add '-1' to each side of the equation.
1 + 8x + -1 + 16x2 = 1 + -6x + -1 + 9x2

Reorder the terms:
1 + -1 + 8x + 16x2 = 1 + -6x + -1 + 9x2

Combine like terms: 1 + -1 = 0
0 + 8x + 16x2 = 1 + -6x + -1 + 9x2
8x + 16x2 = 1 + -6x + -1 + 9x2

Reorder the terms:
8x + 16x2 = 1 + -1 + -6x + 9x2

Combine like terms: 1 + -1 = 0
8x + 16x2 = 0 + -6x + 9x2
8x + 16x2 = -6x + 9x2

Solving
8x + 16x2 = -6x + 9x2

Solving for variable 'x'.

Reorder the terms:
8x + 6x + 16x2 + -9x2 = -6x + 9x2 + 6x + -9x2

Combine like terms: 8x + 6x = 14x
14x + 16x2 + -9x2 = -6x + 9x2 + 6x + -9x2

Combine like terms: 16x2 + -9x2 = 7x2
14x + 7x2 = -6x + 9x2 + 6x + -9x2

Reorder the terms:
14x + 7x2 = -6x + 6x + 9x2 + -9x2

Combine like terms: -6x + 6x = 0
14x + 7x2 = 0 + 9x2 + -9x2
14x + 7x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
14x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(2 + x) = 0

Ignore the factor 7.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -2}

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