(5x-6)(2x+3)+(2x+3)(3x-2)=2x(8x+1)

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Solution for (5x-6)(2x+3)+(2x+3)(3x-2)=2x(8x+1) equation: 


Simplifying
(5x + -6)(2x + 3) + (2x + 3)(3x + -2) = 2x(8x + 1)

Reorder the terms:
(-6 + 5x)(2x + 3) + (2x + 3)(3x + -2) = 2x(8x + 1)

Reorder the terms:
(-6 + 5x)(3 + 2x) + (2x + 3)(3x + -2) = 2x(8x + 1)

Multiply (-6 + 5x) * (3 + 2x)
(-6(3 + 2x) + 5x * (3 + 2x)) + (2x + 3)(3x + -2) = 2x(8x + 1)
((3 * -6 + 2x * -6) + 5x * (3 + 2x)) + (2x + 3)(3x + -2) = 2x(8x + 1)
((-18 + -12x) + 5x * (3 + 2x)) + (2x + 3)(3x + -2) = 2x(8x + 1)
(-18 + -12x + (3 * 5x + 2x * 5x)) + (2x + 3)(3x + -2) = 2x(8x + 1)
(-18 + -12x + (15x + 10x2)) + (2x + 3)(3x + -2) = 2x(8x + 1)

Combine like terms: -12x + 15x = 3x
(-18 + 3x + 10x2) + (2x + 3)(3x + -2) = 2x(8x + 1)

Reorder the terms:
-18 + 3x + 10x2 + (3 + 2x)(3x + -2) = 2x(8x + 1)

Reorder the terms:
-18 + 3x + 10x2 + (3 + 2x)(-2 + 3x) = 2x(8x + 1)

Multiply (3 + 2x) * (-2 + 3x)
-18 + 3x + 10x2 + (3(-2 + 3x) + 2x * (-2 + 3x)) = 2x(8x + 1)
-18 + 3x + 10x2 + ((-2 * 3 + 3x * 3) + 2x * (-2 + 3x)) = 2x(8x + 1)
-18 + 3x + 10x2 + ((-6 + 9x) + 2x * (-2 + 3x)) = 2x(8x + 1)
-18 + 3x + 10x2 + (-6 + 9x + (-2 * 2x + 3x * 2x)) = 2x(8x + 1)
-18 + 3x + 10x2 + (-6 + 9x + (-4x + 6x2)) = 2x(8x + 1)

Combine like terms: 9x + -4x = 5x
-18 + 3x + 10x2 + (-6 + 5x + 6x2) = 2x(8x + 1)

Reorder the terms:
-18 + -6 + 3x + 5x + 10x2 + 6x2 = 2x(8x + 1)

Combine like terms: -18 + -6 = -24
-24 + 3x + 5x + 10x2 + 6x2 = 2x(8x + 1)

Combine like terms: 3x + 5x = 8x
-24 + 8x + 10x2 + 6x2 = 2x(8x + 1)

Combine like terms: 10x2 + 6x2 = 16x2
-24 + 8x + 16x2 = 2x(8x + 1)

Reorder the terms:
-24 + 8x + 16x2 = 2x(1 + 8x)
-24 + 8x + 16x2 = (1 * 2x + 8x * 2x)
-24 + 8x + 16x2 = (2x + 16x2)

Add '-16x2' to each side of the equation.
-24 + 8x + 16x2 + -16x2 = 2x + 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-24 + 8x + 0 = 2x + 16x2 + -16x2
-24 + 8x = 2x + 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-24 + 8x = 2x + 0
-24 + 8x = 2x

Solving
-24 + 8x = 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-24 + 8x + -2x = 2x + -2x

Combine like terms: 8x + -2x = 6x
-24 + 6x = 2x + -2x

Combine like terms: 2x + -2x = 0
-24 + 6x = 0

Add '24' to each side of the equation.
-24 + 24 + 6x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 6x = 0 + 24
6x = 0 + 24

Combine like terms: 0 + 24 = 24
6x = 24

Divide each side by '6'.
x = 4

Simplifying
x = 4

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