(x+5)(137-x)=x(130-x)+91

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Solution for (x+5)(137-x)=x(130-x)+91 equation: 


Simplifying
(x + 5)(137 + -1x) = x(130 + -1x) + 91

Reorder the terms:
(5 + x)(137 + -1x) = x(130 + -1x) + 91

Multiply (5 + x) * (137 + -1x)
(5(137 + -1x) + x(137 + -1x)) = x(130 + -1x) + 91
((137 * 5 + -1x * 5) + x(137 + -1x)) = x(130 + -1x) + 91
((685 + -5x) + x(137 + -1x)) = x(130 + -1x) + 91
(685 + -5x + (137 * x + -1x * x)) = x(130 + -1x) + 91
(685 + -5x + (137x + -1x2)) = x(130 + -1x) + 91

Combine like terms: -5x + 137x = 132x
(685 + 132x + -1x2) = x(130 + -1x) + 91
685 + 132x + -1x2 = (130 * x + -1x * x) + 91
685 + 132x + -1x2 = (130x + -1x2) + 91

Reorder the terms:
685 + 132x + -1x2 = 91 + 130x + -1x2

Add 'x2' to each side of the equation.
685 + 132x + -1x2 + x2 = 91 + 130x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
685 + 132x + 0 = 91 + 130x + -1x2 + x2
685 + 132x = 91 + 130x + -1x2 + x2

Combine like terms: -1x2 + x2 = 0
685 + 132x = 91 + 130x + 0
685 + 132x = 91 + 130x

Solving
685 + 132x = 91 + 130x

Solving for variable 'x'.

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

Add '-130x' to each side of the equation.
685 + 132x + -130x = 91 + 130x + -130x

Combine like terms: 132x + -130x = 2x
685 + 2x = 91 + 130x + -130x

Combine like terms: 130x + -130x = 0
685 + 2x = 91 + 0
685 + 2x = 91

Add '-685' to each side of the equation.
685 + -685 + 2x = 91 + -685

Combine like terms: 685 + -685 = 0
0 + 2x = 91 + -685
2x = 91 + -685

Combine like terms: 91 + -685 = -594
2x = -594

Divide each side by '2'.
x = -297

Simplifying
x = -297

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