3[2(j-2)-7(2j-3)]-5[4(2j-5)-(3j-2)]=6(j+1)+1

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


Simplifying
3[2(j + -2) + -7(2j + -3)] + -5[4(2j + -5) + -1(3j + -2)] = 6(j + 1) + 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
141 + -61j = 7 + 6j

Solving for variable 'j'.

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

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

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

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

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

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

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

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

Simplifying
j = 2

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