(x+2)(7-x)=(4+x)(5-x)

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Solution for (x+2)(7-x)=(4+x)(5-x) equation: 


Simplifying
(x + 2)(7 + -1x) = (4 + x)(5 + -1x)

Reorder the terms:
(2 + x)(7 + -1x) = (4 + x)(5 + -1x)

Multiply (2 + x) * (7 + -1x)
(2(7 + -1x) + x(7 + -1x)) = (4 + x)(5 + -1x)
((7 * 2 + -1x * 2) + x(7 + -1x)) = (4 + x)(5 + -1x)
((14 + -2x) + x(7 + -1x)) = (4 + x)(5 + -1x)
(14 + -2x + (7 * x + -1x * x)) = (4 + x)(5 + -1x)
(14 + -2x + (7x + -1x2)) = (4 + x)(5 + -1x)

Combine like terms: -2x + 7x = 5x
(14 + 5x + -1x2) = (4 + x)(5 + -1x)

Multiply (4 + x) * (5 + -1x)
14 + 5x + -1x2 = (4(5 + -1x) + x(5 + -1x))
14 + 5x + -1x2 = ((5 * 4 + -1x * 4) + x(5 + -1x))
14 + 5x + -1x2 = ((20 + -4x) + x(5 + -1x))
14 + 5x + -1x2 = (20 + -4x + (5 * x + -1x * x))
14 + 5x + -1x2 = (20 + -4x + (5x + -1x2))

Combine like terms: -4x + 5x = 1x
14 + 5x + -1x2 = (20 + 1x + -1x2)

Add 'x2' to each side of the equation.
14 + 5x + -1x2 + x2 = 20 + 1x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
14 + 5x + 0 = 20 + 1x + -1x2 + x2
14 + 5x = 20 + 1x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
14 + 5x = 20 + 1x + 0
14 + 5x = 20 + 1x

Solving
14 + 5x = 20 + 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.
14 + 5x + -1x = 20 + 1x + -1x

Combine like terms: 5x + -1x = 4x
14 + 4x = 20 + 1x + -1x

Combine like terms: 1x + -1x = 0
14 + 4x = 20 + 0
14 + 4x = 20

Add '-14' to each side of the equation.
14 + -14 + 4x = 20 + -14

Combine like terms: 14 + -14 = 0
0 + 4x = 20 + -14
4x = 20 + -14

Combine like terms: 20 + -14 = 6
4x = 6

Divide each side by '4'.
x = 1.5

Simplifying
x = 1.5

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