(2X-1)(X+3)+(2X-1)(2X+1)=0

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Solution for (2X-1)(X+3)+(2X-1)(2X+1)=0 equation: 


Simplifying
(2X + -1)(X + 3) + (2X + -1)(2X + 1) = 0

Reorder the terms:
(-1 + 2X)(X + 3) + (2X + -1)(2X + 1) = 0

Reorder the terms:
(-1 + 2X)(3 + X) + (2X + -1)(2X + 1) = 0

Multiply (-1 + 2X) * (3 + X)
(-1(3 + X) + 2X * (3 + X)) + (2X + -1)(2X + 1) = 0
((3 * -1 + X * -1) + 2X * (3 + X)) + (2X + -1)(2X + 1) = 0
((-3 + -1X) + 2X * (3 + X)) + (2X + -1)(2X + 1) = 0
(-3 + -1X + (3 * 2X + X * 2X)) + (2X + -1)(2X + 1) = 0
(-3 + -1X + (6X + 2X2)) + (2X + -1)(2X + 1) = 0

Combine like terms: -1X + 6X = 5X
(-3 + 5X + 2X2) + (2X + -1)(2X + 1) = 0

Reorder the terms:
-3 + 5X + 2X2 + (-1 + 2X)(2X + 1) = 0

Reorder the terms:
-3 + 5X + 2X2 + (-1 + 2X)(1 + 2X) = 0

Multiply (-1 + 2X) * (1 + 2X)
-3 + 5X + 2X2 + (-1(1 + 2X) + 2X * (1 + 2X)) = 0
-3 + 5X + 2X2 + ((1 * -1 + 2X * -1) + 2X * (1 + 2X)) = 0
-3 + 5X + 2X2 + ((-1 + -2X) + 2X * (1 + 2X)) = 0
-3 + 5X + 2X2 + (-1 + -2X + (1 * 2X + 2X * 2X)) = 0
-3 + 5X + 2X2 + (-1 + -2X + (2X + 4X2)) = 0

Combine like terms: -2X + 2X = 0
-3 + 5X + 2X2 + (-1 + 0 + 4X2) = 0
-3 + 5X + 2X2 + (-1 + 4X2) = 0

Reorder the terms:
-3 + -1 + 5X + 2X2 + 4X2 = 0

Combine like terms: -3 + -1 = -4
-4 + 5X + 2X2 + 4X2 = 0

Combine like terms: 2X2 + 4X2 = 6X2
-4 + 5X + 6X2 = 0

Solving
-4 + 5X + 6X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-4 + -3X)(1 + -2X) = 0


Subproblem 1
Set the factor '(-4 + -3X)' equal to zero and attempt to solve:

Simplifying
-4 + -3X = 0

Solving
-4 + -3X = 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 + -3X = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3X = 0 + 4
-3X = 0 + 4

Combine like terms: 0 + 4 = 4
-3X = 4

Divide each side by '-3'.
X = -1.333333333

Simplifying
X = -1.333333333

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 = {-1.333333333, 0.5}

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