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

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


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

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

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

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

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

Multiply (1 + -1x) * (5 + -1x)
4 + 9x + 2x2 = 2(1(5 + -1x) + -1x * (5 + -1x))
4 + 9x + 2x2 = 2((5 * 1 + -1x * 1) + -1x * (5 + -1x))
4 + 9x + 2x2 = 2((5 + -1x) + -1x * (5 + -1x))
4 + 9x + 2x2 = 2(5 + -1x + (5 * -1x + -1x * -1x))
4 + 9x + 2x2 = 2(5 + -1x + (-5x + 1x2))

Combine like terms: -1x + -5x = -6x
4 + 9x + 2x2 = 2(5 + -6x + 1x2)
4 + 9x + 2x2 = (5 * 2 + -6x * 2 + 1x2 * 2)
4 + 9x + 2x2 = (10 + -12x + 2x2)

Add '-2x2' to each side of the equation.
4 + 9x + 2x2 + -2x2 = 10 + -12x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + 9x + 0 = 10 + -12x + 2x2 + -2x2
4 + 9x = 10 + -12x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + 9x = 10 + -12x + 0
4 + 9x = 10 + -12x

Solving
4 + 9x = 10 + -12x

Solving for variable 'x'.

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

Add '12x' to each side of the equation.
4 + 9x + 12x = 10 + -12x + 12x

Combine like terms: 9x + 12x = 21x
4 + 21x = 10 + -12x + 12x

Combine like terms: -12x + 12x = 0
4 + 21x = 10 + 0
4 + 21x = 10

Add '-4' to each side of the equation.
4 + -4 + 21x = 10 + -4

Combine like terms: 4 + -4 = 0
0 + 21x = 10 + -4
21x = 10 + -4

Combine like terms: 10 + -4 = 6
21x = 6

Divide each side by '21'.
x = 0.2857142857

Simplifying
x = 0.2857142857

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