(x-3)-(2x-7)+6=13(x-1)+4(2x+1)-7x

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Solution for (x-3)-(2x-7)+6=13(x-1)+4(2x+1)-7x equation: 


Simplifying
(x + -3) + -1(2x + -7) + 6 = 13(x + -1) + 4(2x + 1) + -7x

Reorder the terms:
(-3 + x) + -1(2x + -7) + 6 = 13(x + -1) + 4(2x + 1) + -7x

Remove parenthesis around (-3 + x)
-3 + x + -1(2x + -7) + 6 = 13(x + -1) + 4(2x + 1) + -7x

Reorder the terms:
-3 + x + -1(-7 + 2x) + 6 = 13(x + -1) + 4(2x + 1) + -7x
-3 + x + (-7 * -1 + 2x * -1) + 6 = 13(x + -1) + 4(2x + 1) + -7x
-3 + x + (7 + -2x) + 6 = 13(x + -1) + 4(2x + 1) + -7x

Reorder the terms:
-3 + 7 + 6 + x + -2x = 13(x + -1) + 4(2x + 1) + -7x

Combine like terms: -3 + 7 = 4
4 + 6 + x + -2x = 13(x + -1) + 4(2x + 1) + -7x

Combine like terms: 4 + 6 = 10
10 + x + -2x = 13(x + -1) + 4(2x + 1) + -7x

Combine like terms: x + -2x = -1x
10 + -1x = 13(x + -1) + 4(2x + 1) + -7x

Reorder the terms:
10 + -1x = 13(-1 + x) + 4(2x + 1) + -7x
10 + -1x = (-1 * 13 + x * 13) + 4(2x + 1) + -7x
10 + -1x = (-13 + 13x) + 4(2x + 1) + -7x

Reorder the terms:
10 + -1x = -13 + 13x + 4(1 + 2x) + -7x
10 + -1x = -13 + 13x + (1 * 4 + 2x * 4) + -7x
10 + -1x = -13 + 13x + (4 + 8x) + -7x

Reorder the terms:
10 + -1x = -13 + 4 + 13x + 8x + -7x

Combine like terms: -13 + 4 = -9
10 + -1x = -9 + 13x + 8x + -7x

Combine like terms: 13x + 8x = 21x
10 + -1x = -9 + 21x + -7x

Combine like terms: 21x + -7x = 14x
10 + -1x = -9 + 14x

Solving
10 + -1x = -9 + 14x

Solving for variable 'x'.

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

Add '-14x' to each side of the equation.
10 + -1x + -14x = -9 + 14x + -14x

Combine like terms: -1x + -14x = -15x
10 + -15x = -9 + 14x + -14x

Combine like terms: 14x + -14x = 0
10 + -15x = -9 + 0
10 + -15x = -9

Add '-10' to each side of the equation.
10 + -10 + -15x = -9 + -10

Combine like terms: 10 + -10 = 0
0 + -15x = -9 + -10
-15x = -9 + -10

Combine like terms: -9 + -10 = -19
-15x = -19

Divide each side by '-15'.
x = 1.266666667

Simplifying
x = 1.266666667

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