(4x+3)(2x+3)-(2x-5)(4x-1)=0

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Solution for (4x+3)(2x+3)-(2x-5)(4x-1)=0 equation: 


Simplifying
(4x + 3)(2x + 3) + -1(2x + -5)(4x + -1) = 0

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

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

Multiply (3 + 4x) * (3 + 2x)
(3(3 + 2x) + 4x * (3 + 2x)) + -1(2x + -5)(4x + -1) = 0
((3 * 3 + 2x * 3) + 4x * (3 + 2x)) + -1(2x + -5)(4x + -1) = 0
((9 + 6x) + 4x * (3 + 2x)) + -1(2x + -5)(4x + -1) = 0
(9 + 6x + (3 * 4x + 2x * 4x)) + -1(2x + -5)(4x + -1) = 0
(9 + 6x + (12x + 8x2)) + -1(2x + -5)(4x + -1) = 0

Combine like terms: 6x + 12x = 18x
(9 + 18x + 8x2) + -1(2x + -5)(4x + -1) = 0

Reorder the terms:
9 + 18x + 8x2 + -1(-5 + 2x)(4x + -1) = 0

Reorder the terms:
9 + 18x + 8x2 + -1(-5 + 2x)(-1 + 4x) = 0

Multiply (-5 + 2x) * (-1 + 4x)
9 + 18x + 8x2 + -1(-5(-1 + 4x) + 2x * (-1 + 4x)) = 0
9 + 18x + 8x2 + -1((-1 * -5 + 4x * -5) + 2x * (-1 + 4x)) = 0
9 + 18x + 8x2 + -1((5 + -20x) + 2x * (-1 + 4x)) = 0
9 + 18x + 8x2 + -1(5 + -20x + (-1 * 2x + 4x * 2x)) = 0
9 + 18x + 8x2 + -1(5 + -20x + (-2x + 8x2)) = 0

Combine like terms: -20x + -2x = -22x
9 + 18x + 8x2 + -1(5 + -22x + 8x2) = 0
9 + 18x + 8x2 + (5 * -1 + -22x * -1 + 8x2 * -1) = 0
9 + 18x + 8x2 + (-5 + 22x + -8x2) = 0

Reorder the terms:
9 + -5 + 18x + 22x + 8x2 + -8x2 = 0

Combine like terms: 9 + -5 = 4
4 + 18x + 22x + 8x2 + -8x2 = 0

Combine like terms: 18x + 22x = 40x
4 + 40x + 8x2 + -8x2 = 0

Combine like terms: 8x2 + -8x2 = 0
4 + 40x + 0 = 0
4 + 40x = 0

Solving
4 + 40x = 0

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + 40x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 40x = 0 + -4
40x = 0 + -4

Combine like terms: 0 + -4 = -4
40x = -4

Divide each side by '40'.
x = -0.1

Simplifying
x = -0.1

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