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

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


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

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

Multiply (3 + x) * (4 + -1x)
2(3(4 + -1x) + x(4 + -1x)) = (2 + x)(5 + -2x)
2((4 * 3 + -1x * 3) + x(4 + -1x)) = (2 + x)(5 + -2x)
2((12 + -3x) + x(4 + -1x)) = (2 + x)(5 + -2x)
2(12 + -3x + (4 * x + -1x * x)) = (2 + x)(5 + -2x)
2(12 + -3x + (4x + -1x2)) = (2 + x)(5 + -2x)

Combine like terms: -3x + 4x = 1x
2(12 + 1x + -1x2) = (2 + x)(5 + -2x)
(12 * 2 + 1x * 2 + -1x2 * 2) = (2 + x)(5 + -2x)
(24 + 2x + -2x2) = (2 + x)(5 + -2x)

Multiply (2 + x) * (5 + -2x)
24 + 2x + -2x2 = (2(5 + -2x) + x(5 + -2x))
24 + 2x + -2x2 = ((5 * 2 + -2x * 2) + x(5 + -2x))
24 + 2x + -2x2 = ((10 + -4x) + x(5 + -2x))
24 + 2x + -2x2 = (10 + -4x + (5 * x + -2x * x))
24 + 2x + -2x2 = (10 + -4x + (5x + -2x2))

Combine like terms: -4x + 5x = 1x
24 + 2x + -2x2 = (10 + 1x + -2x2)

Add '2x2' to each side of the equation.
24 + 2x + -2x2 + 2x2 = 10 + 1x + -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
24 + 2x + 0 = 10 + 1x + -2x2 + 2x2
24 + 2x = 10 + 1x + -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
24 + 2x = 10 + 1x + 0
24 + 2x = 10 + 1x

Solving
24 + 2x = 10 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
24 + 2x + -1x = 10 + 1x + -1x

Combine like terms: 2x + -1x = 1x
24 + 1x = 10 + 1x + -1x

Combine like terms: 1x + -1x = 0
24 + 1x = 10 + 0
24 + 1x = 10

Add '-24' to each side of the equation.
24 + -24 + 1x = 10 + -24

Combine like terms: 24 + -24 = 0
0 + 1x = 10 + -24
1x = 10 + -24

Combine like terms: 10 + -24 = -14
1x = -14

Divide each side by '1'.
x = -14

Simplifying
x = -14

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