(2+x)(7-3x)=(5-4x)(13-x)

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Solution for (2+x)(7-3x)=(5-4x)(13-x) equation: 


Simplifying
(2 + x)(7 + -3x) = (5 + -4x)(13 + -1x)

Multiply (2 + x) * (7 + -3x)
(2(7 + -3x) + x(7 + -3x)) = (5 + -4x)(13 + -1x)
((7 * 2 + -3x * 2) + x(7 + -3x)) = (5 + -4x)(13 + -1x)
((14 + -6x) + x(7 + -3x)) = (5 + -4x)(13 + -1x)
(14 + -6x + (7 * x + -3x * x)) = (5 + -4x)(13 + -1x)
(14 + -6x + (7x + -3x2)) = (5 + -4x)(13 + -1x)

Combine like terms: -6x + 7x = 1x
(14 + 1x + -3x2) = (5 + -4x)(13 + -1x)

Multiply (5 + -4x) * (13 + -1x)
14 + 1x + -3x2 = (5(13 + -1x) + -4x * (13 + -1x))
14 + 1x + -3x2 = ((13 * 5 + -1x * 5) + -4x * (13 + -1x))
14 + 1x + -3x2 = ((65 + -5x) + -4x * (13 + -1x))
14 + 1x + -3x2 = (65 + -5x + (13 * -4x + -1x * -4x))
14 + 1x + -3x2 = (65 + -5x + (-52x + 4x2))

Combine like terms: -5x + -52x = -57x
14 + 1x + -3x2 = (65 + -57x + 4x2)

Solving
14 + 1x + -3x2 = 65 + -57x + 4x2

Solving for variable 'x'.

Reorder the terms:
14 + -65 + 1x + 57x + -3x2 + -4x2 = 65 + -57x + 4x2 + -65 + 57x + -4x2

Combine like terms: 14 + -65 = -51
-51 + 1x + 57x + -3x2 + -4x2 = 65 + -57x + 4x2 + -65 + 57x + -4x2

Combine like terms: 1x + 57x = 58x
-51 + 58x + -3x2 + -4x2 = 65 + -57x + 4x2 + -65 + 57x + -4x2

Combine like terms: -3x2 + -4x2 = -7x2
-51 + 58x + -7x2 = 65 + -57x + 4x2 + -65 + 57x + -4x2

Reorder the terms:
-51 + 58x + -7x2 = 65 + -65 + -57x + 57x + 4x2 + -4x2

Combine like terms: 65 + -65 = 0
-51 + 58x + -7x2 = 0 + -57x + 57x + 4x2 + -4x2
-51 + 58x + -7x2 = -57x + 57x + 4x2 + -4x2

Combine like terms: -57x + 57x = 0
-51 + 58x + -7x2 = 0 + 4x2 + -4x2
-51 + 58x + -7x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-51 + 58x + -7x2 = 0

Factor a trinomial.
(-51 + 7x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-51 + 7x)' equal to zero and attempt to solve:

Simplifying
-51 + 7x = 0

Solving
-51 + 7x = 0

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

Add '51' to each side of the equation.
-51 + 51 + 7x = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 7x = 0 + 51
7x = 0 + 51

Combine like terms: 0 + 51 = 51
7x = 51

Divide each side by '7'.
x = 7.285714286

Simplifying
x = 7.285714286

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {7.285714286, 1}

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