3(2(x-2)-7(2x-3))-5(4(2x-5)-(3x-2))=6(x+1)+1

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Solution for 3(2(x-2)-7(2x-3))-5(4(2x-5)-(3x-2))=6(x+1)+1 equation: 


Simplifying
3(2(x + -2) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1

Reorder the terms:
3(2(-2 + x) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1
3((-2 * 2 + x * 2) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1
3((-4 + 2x) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1

Reorder the terms:
3(-4 + 2x + -7(-3 + 2x)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1
3(-4 + 2x + (-3 * -7 + 2x * -7)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1
3(-4 + 2x + (21 + -14x)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1

Reorder the terms:
3(-4 + 21 + 2x + -14x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1

Combine like terms: -4 + 21 = 17
3(17 + 2x + -14x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1

Combine like terms: 2x + -14x = -12x
3(17 + -12x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1
(17 * 3 + -12x * 3) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1
(51 + -36x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1

Reorder the terms:
51 + -36x + -5(4(-5 + 2x) + -1(3x + -2)) = 6(x + 1) + 1
51 + -36x + -5((-5 * 4 + 2x * 4) + -1(3x + -2)) = 6(x + 1) + 1
51 + -36x + -5((-20 + 8x) + -1(3x + -2)) = 6(x + 1) + 1

Reorder the terms:
51 + -36x + -5(-20 + 8x + -1(-2 + 3x)) = 6(x + 1) + 1
51 + -36x + -5(-20 + 8x + (-2 * -1 + 3x * -1)) = 6(x + 1) + 1
51 + -36x + -5(-20 + 8x + (2 + -3x)) = 6(x + 1) + 1

Reorder the terms:
51 + -36x + -5(-20 + 2 + 8x + -3x) = 6(x + 1) + 1

Combine like terms: -20 + 2 = -18
51 + -36x + -5(-18 + 8x + -3x) = 6(x + 1) + 1

Combine like terms: 8x + -3x = 5x
51 + -36x + -5(-18 + 5x) = 6(x + 1) + 1
51 + -36x + (-18 * -5 + 5x * -5) = 6(x + 1) + 1
51 + -36x + (90 + -25x) = 6(x + 1) + 1

Reorder the terms:
51 + 90 + -36x + -25x = 6(x + 1) + 1

Combine like terms: 51 + 90 = 141
141 + -36x + -25x = 6(x + 1) + 1

Combine like terms: -36x + -25x = -61x
141 + -61x = 6(x + 1) + 1

Reorder the terms:
141 + -61x = 6(1 + x) + 1
141 + -61x = (1 * 6 + x * 6) + 1
141 + -61x = (6 + 6x) + 1

Reorder the terms:
141 + -61x = 6 + 1 + 6x

Combine like terms: 6 + 1 = 7
141 + -61x = 7 + 6x

Solving
141 + -61x = 7 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
141 + -61x + -6x = 7 + 6x + -6x

Combine like terms: -61x + -6x = -67x
141 + -67x = 7 + 6x + -6x

Combine like terms: 6x + -6x = 0
141 + -67x = 7 + 0
141 + -67x = 7

Add '-141' to each side of the equation.
141 + -141 + -67x = 7 + -141

Combine like terms: 141 + -141 = 0
0 + -67x = 7 + -141
-67x = 7 + -141

Combine like terms: 7 + -141 = -134
-67x = -134

Divide each side by '-67'.
x = 2

Simplifying
x = 2

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