(1-2x)*(1+2x)=2x-x^2+1

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


Simplifying
(1 + -2x)(1 + 2x) = 2x + -1x2 + 1

Multiply (1 + -2x) * (1 + 2x)
(1(1 + 2x) + -2x * (1 + 2x)) = 2x + -1x2 + 1
((1 * 1 + 2x * 1) + -2x * (1 + 2x)) = 2x + -1x2 + 1
((1 + 2x) + -2x * (1 + 2x)) = 2x + -1x2 + 1
(1 + 2x + (1 * -2x + 2x * -2x)) = 2x + -1x2 + 1
(1 + 2x + (-2x + -4x2)) = 2x + -1x2 + 1

Combine like terms: 2x + -2x = 0
(1 + 0 + -4x2) = 2x + -1x2 + 1
(1 + -4x2) = 2x + -1x2 + 1

Reorder the terms:
1 + -4x2 = 1 + 2x + -1x2

Add '-1' to each side of the equation.
1 + -1 + -4x2 = 1 + 2x + -1 + -1x2

Combine like terms: 1 + -1 = 0
0 + -4x2 = 1 + 2x + -1 + -1x2
-4x2 = 1 + 2x + -1 + -1x2

Reorder the terms:
-4x2 = 1 + -1 + 2x + -1x2

Combine like terms: 1 + -1 = 0
-4x2 = 0 + 2x + -1x2
-4x2 = 2x + -1x2

Solving
-4x2 = 2x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2x + -4x2 + x2 = 2x + -1x2 + -2x + x2

Combine like terms: -4x2 + x2 = -3x2
-2x + -3x2 = 2x + -1x2 + -2x + x2

Reorder the terms:
-2x + -3x2 = 2x + -2x + -1x2 + x2

Combine like terms: 2x + -2x = 0
-2x + -3x2 = 0 + -1x2 + x2
-2x + -3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(2 + 3x) = 0

Ignore the factor -1.

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 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -0.6666666667}

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