3(3x+1)-4(2x-5)=5(x-1)-2(10-x)

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Solution for 3(3x+1)-4(2x-5)=5(x-1)-2(10-x) equation: 


Simplifying
3(3x + 1) + -4(2x + -5) = 5(x + -1) + -2(10 + -1x)

Reorder the terms:
3(1 + 3x) + -4(2x + -5) = 5(x + -1) + -2(10 + -1x)
(1 * 3 + 3x * 3) + -4(2x + -5) = 5(x + -1) + -2(10 + -1x)
(3 + 9x) + -4(2x + -5) = 5(x + -1) + -2(10 + -1x)

Reorder the terms:
3 + 9x + -4(-5 + 2x) = 5(x + -1) + -2(10 + -1x)
3 + 9x + (-5 * -4 + 2x * -4) = 5(x + -1) + -2(10 + -1x)
3 + 9x + (20 + -8x) = 5(x + -1) + -2(10 + -1x)

Reorder the terms:
3 + 20 + 9x + -8x = 5(x + -1) + -2(10 + -1x)

Combine like terms: 3 + 20 = 23
23 + 9x + -8x = 5(x + -1) + -2(10 + -1x)

Combine like terms: 9x + -8x = 1x
23 + 1x = 5(x + -1) + -2(10 + -1x)

Reorder the terms:
23 + 1x = 5(-1 + x) + -2(10 + -1x)
23 + 1x = (-1 * 5 + x * 5) + -2(10 + -1x)
23 + 1x = (-5 + 5x) + -2(10 + -1x)
23 + 1x = -5 + 5x + (10 * -2 + -1x * -2)
23 + 1x = -5 + 5x + (-20 + 2x)

Reorder the terms:
23 + 1x = -5 + -20 + 5x + 2x

Combine like terms: -5 + -20 = -25
23 + 1x = -25 + 5x + 2x

Combine like terms: 5x + 2x = 7x
23 + 1x = -25 + 7x

Solving
23 + 1x = -25 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
23 + 1x + -7x = -25 + 7x + -7x

Combine like terms: 1x + -7x = -6x
23 + -6x = -25 + 7x + -7x

Combine like terms: 7x + -7x = 0
23 + -6x = -25 + 0
23 + -6x = -25

Add '-23' to each side of the equation.
23 + -23 + -6x = -25 + -23

Combine like terms: 23 + -23 = 0
0 + -6x = -25 + -23
-6x = -25 + -23

Combine like terms: -25 + -23 = -48
-6x = -48

Divide each side by '-6'.
x = 8

Simplifying
x = 8

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