16x^2-1=(4x+1)(x-1)

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Solution for 16x^2-1=(4x+1)(x-1) equation: 


Simplifying
16x2 + -1 = (4x + 1)(x + -1)

Reorder the terms:
-1 + 16x2 = (4x + 1)(x + -1)

Reorder the terms:
-1 + 16x2 = (1 + 4x)(x + -1)

Reorder the terms:
-1 + 16x2 = (1 + 4x)(-1 + x)

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

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

Add '1' to each side of the equation.
-1 + 1 + 16x2 = -1 + -3x + 1 + 4x2

Combine like terms: -1 + 1 = 0
0 + 16x2 = -1 + -3x + 1 + 4x2
16x2 = -1 + -3x + 1 + 4x2

Reorder the terms:
16x2 = -1 + 1 + -3x + 4x2

Combine like terms: -1 + 1 = 0
16x2 = 0 + -3x + 4x2
16x2 = -3x + 4x2

Solving
16x2 = -3x + 4x2

Solving for variable 'x'.

Reorder the terms:
3x + 16x2 + -4x2 = -3x + 4x2 + 3x + -4x2

Combine like terms: 16x2 + -4x2 = 12x2
3x + 12x2 = -3x + 4x2 + 3x + -4x2

Reorder the terms:
3x + 12x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
3x + 12x2 = 0 + 4x2 + -4x2
3x + 12x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 4x) = 0

Ignore the factor 3.

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 '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {0, -0.25}

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