(3x+1)(2x+5)=(2-6x)(4-x)

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Solution for (3x+1)(2x+5)=(2-6x)(4-x) equation: 


Simplifying
(3x + 1)(2x + 5) = (2 + -6x)(4 + -1x)

Reorder the terms:
(1 + 3x)(2x + 5) = (2 + -6x)(4 + -1x)

Reorder the terms:
(1 + 3x)(5 + 2x) = (2 + -6x)(4 + -1x)

Multiply (1 + 3x) * (5 + 2x)
(1(5 + 2x) + 3x * (5 + 2x)) = (2 + -6x)(4 + -1x)
((5 * 1 + 2x * 1) + 3x * (5 + 2x)) = (2 + -6x)(4 + -1x)
((5 + 2x) + 3x * (5 + 2x)) = (2 + -6x)(4 + -1x)
(5 + 2x + (5 * 3x + 2x * 3x)) = (2 + -6x)(4 + -1x)
(5 + 2x + (15x + 6x2)) = (2 + -6x)(4 + -1x)

Combine like terms: 2x + 15x = 17x
(5 + 17x + 6x2) = (2 + -6x)(4 + -1x)

Multiply (2 + -6x) * (4 + -1x)
5 + 17x + 6x2 = (2(4 + -1x) + -6x * (4 + -1x))
5 + 17x + 6x2 = ((4 * 2 + -1x * 2) + -6x * (4 + -1x))
5 + 17x + 6x2 = ((8 + -2x) + -6x * (4 + -1x))
5 + 17x + 6x2 = (8 + -2x + (4 * -6x + -1x * -6x))
5 + 17x + 6x2 = (8 + -2x + (-24x + 6x2))

Combine like terms: -2x + -24x = -26x
5 + 17x + 6x2 = (8 + -26x + 6x2)

Add '-6x2' to each side of the equation.
5 + 17x + 6x2 + -6x2 = 8 + -26x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 17x + 0 = 8 + -26x + 6x2 + -6x2
5 + 17x = 8 + -26x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 17x = 8 + -26x + 0
5 + 17x = 8 + -26x

Solving
5 + 17x = 8 + -26x

Solving for variable 'x'.

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

Add '26x' to each side of the equation.
5 + 17x + 26x = 8 + -26x + 26x

Combine like terms: 17x + 26x = 43x
5 + 43x = 8 + -26x + 26x

Combine like terms: -26x + 26x = 0
5 + 43x = 8 + 0
5 + 43x = 8

Add '-5' to each side of the equation.
5 + -5 + 43x = 8 + -5

Combine like terms: 5 + -5 = 0
0 + 43x = 8 + -5
43x = 8 + -5

Combine like terms: 8 + -5 = 3
43x = 3

Divide each side by '43'.
x = 0.06976744186

Simplifying
x = 0.06976744186

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