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

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


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

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

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

Multiply (3 + 2x) * (3 + 2x)
4(3(3 + 2x) + 2x * (3 + 2x)) + -1(2x + 3) + -3 = 0
4((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + -1(2x + 3) + -3 = 0
4((9 + 6x) + 2x * (3 + 2x)) + -1(2x + 3) + -3 = 0
4(9 + 6x + (3 * 2x + 2x * 2x)) + -1(2x + 3) + -3 = 0
4(9 + 6x + (6x + 4x2)) + -1(2x + 3) + -3 = 0

Combine like terms: 6x + 6x = 12x
4(9 + 12x + 4x2) + -1(2x + 3) + -3 = 0
(9 * 4 + 12x * 4 + 4x2 * 4) + -1(2x + 3) + -3 = 0
(36 + 48x + 16x2) + -1(2x + 3) + -3 = 0

Reorder the terms:
36 + 48x + 16x2 + -1(3 + 2x) + -3 = 0
36 + 48x + 16x2 + (3 * -1 + 2x * -1) + -3 = 0
36 + 48x + 16x2 + (-3 + -2x) + -3 = 0

Reorder the terms:
36 + -3 + -3 + 48x + -2x + 16x2 = 0

Combine like terms: 36 + -3 = 33
33 + -3 + 48x + -2x + 16x2 = 0

Combine like terms: 33 + -3 = 30
30 + 48x + -2x + 16x2 = 0

Combine like terms: 48x + -2x = 46x
30 + 46x + 16x2 = 0

Solving
30 + 46x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 23x + 8x2) = 0

Factor a trinomial.
2((15 + 8x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 8x)' equal to zero and attempt to solve:

Simplifying
15 + 8x = 0

Solving
15 + 8x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 8x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 8x = 0 + -15
8x = 0 + -15

Combine like terms: 0 + -15 = -15
8x = -15

Divide each side by '8'.
x = -1.875

Simplifying
x = -1.875

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-1.875, -1}

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