(2x+1)(2x+1)-3(2x+1)-4=0

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Solution for (2x+1)(2x+1)-3(2x+1)-4=0 equation: 


Simplifying
(2x + 1)(2x + 1) + -3(2x + 1) + -4 = 0

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

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

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

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

Reorder the terms:
1 + 4x + 4x2 + -3(1 + 2x) + -4 = 0
1 + 4x + 4x2 + (1 * -3 + 2x * -3) + -4 = 0
1 + 4x + 4x2 + (-3 + -6x) + -4 = 0

Reorder the terms:
1 + -3 + -4 + 4x + -6x + 4x2 = 0

Combine like terms: 1 + -3 = -2
-2 + -4 + 4x + -6x + 4x2 = 0

Combine like terms: -2 + -4 = -6
-6 + 4x + -6x + 4x2 = 0

Combine like terms: 4x + -6x = -2x
-6 + -2x + 4x2 = 0

Solving
-6 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}

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