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

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


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

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

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

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) + -1(x + -3)(2x + 1) = 0
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -1(x + -3)(2x + 1) = 0
((1 + 2x) + 2x * (1 + 2x)) + -1(x + -3)(2x + 1) = 0
(1 + 2x + (1 * 2x + 2x * 2x)) + -1(x + -3)(2x + 1) = 0
(1 + 2x + (2x + 4x2)) + -1(x + -3)(2x + 1) = 0

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) + -1(x + -3)(2x + 1) = 0

Reorder the terms:
1 + 4x + 4x2 + -1(-3 + x)(2x + 1) = 0

Reorder the terms:
1 + 4x + 4x2 + -1(-3 + x)(1 + 2x) = 0

Multiply (-3 + x) * (1 + 2x)
1 + 4x + 4x2 + -1(-3(1 + 2x) + x(1 + 2x)) = 0
1 + 4x + 4x2 + -1((1 * -3 + 2x * -3) + x(1 + 2x)) = 0
1 + 4x + 4x2 + -1((-3 + -6x) + x(1 + 2x)) = 0
1 + 4x + 4x2 + -1(-3 + -6x + (1 * x + 2x * x)) = 0
1 + 4x + 4x2 + -1(-3 + -6x + (1x + 2x2)) = 0

Combine like terms: -6x + 1x = -5x
1 + 4x + 4x2 + -1(-3 + -5x + 2x2) = 0
1 + 4x + 4x2 + (-3 * -1 + -5x * -1 + 2x2 * -1) = 0
1 + 4x + 4x2 + (3 + 5x + -2x2) = 0

Reorder the terms:
1 + 3 + 4x + 5x + 4x2 + -2x2 = 0

Combine like terms: 1 + 3 = 4
4 + 4x + 5x + 4x2 + -2x2 = 0

Combine like terms: 4x + 5x = 9x
4 + 9x + 4x2 + -2x2 = 0

Combine like terms: 4x2 + -2x2 = 2x2
4 + 9x + 2x2 = 0

Solving
4 + 9x + 2x2 = 0

Solving for variable 'x'.

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


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

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4

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 = {-4, -0.5}

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