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

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


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

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

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

Multiply (3 + 4x) * (3 + 4x)
(3(3 + 4x) + 4x * (3 + 4x)) + -1(2x + 3)(2x + 3) = 0
((3 * 3 + 4x * 3) + 4x * (3 + 4x)) + -1(2x + 3)(2x + 3) = 0
((9 + 12x) + 4x * (3 + 4x)) + -1(2x + 3)(2x + 3) = 0
(9 + 12x + (3 * 4x + 4x * 4x)) + -1(2x + 3)(2x + 3) = 0
(9 + 12x + (12x + 16x2)) + -1(2x + 3)(2x + 3) = 0

Combine like terms: 12x + 12x = 24x
(9 + 24x + 16x2) + -1(2x + 3)(2x + 3) = 0

Reorder the terms:
9 + 24x + 16x2 + -1(3 + 2x)(2x + 3) = 0

Reorder the terms:
9 + 24x + 16x2 + -1(3 + 2x)(3 + 2x) = 0

Multiply (3 + 2x) * (3 + 2x)
9 + 24x + 16x2 + -1(3(3 + 2x) + 2x * (3 + 2x)) = 0
9 + 24x + 16x2 + -1((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 0
9 + 24x + 16x2 + -1((9 + 6x) + 2x * (3 + 2x)) = 0
9 + 24x + 16x2 + -1(9 + 6x + (3 * 2x + 2x * 2x)) = 0
9 + 24x + 16x2 + -1(9 + 6x + (6x + 4x2)) = 0

Combine like terms: 6x + 6x = 12x
9 + 24x + 16x2 + -1(9 + 12x + 4x2) = 0
9 + 24x + 16x2 + (9 * -1 + 12x * -1 + 4x2 * -1) = 0
9 + 24x + 16x2 + (-9 + -12x + -4x2) = 0

Reorder the terms:
9 + -9 + 24x + -12x + 16x2 + -4x2 = 0

Combine like terms: 9 + -9 = 0
0 + 24x + -12x + 16x2 + -4x2 = 0
24x + -12x + 16x2 + -4x2 = 0

Combine like terms: 24x + -12x = 12x
12x + 16x2 + -4x2 = 0

Combine like terms: 16x2 + -4x2 = 12x2
12x + 12x2 = 0

Solving
12x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(1 + x) = 0

Ignore the factor 12.

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 '(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 = {0, -1}

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