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

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


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

Reorder the terms:
10(3 + x) + -2(x + -1) = 4(x + -2) + 3(x + -3)
(3 * 10 + x * 10) + -2(x + -1) = 4(x + -2) + 3(x + -3)
(30 + 10x) + -2(x + -1) = 4(x + -2) + 3(x + -3)

Reorder the terms:
30 + 10x + -2(-1 + x) = 4(x + -2) + 3(x + -3)
30 + 10x + (-1 * -2 + x * -2) = 4(x + -2) + 3(x + -3)
30 + 10x + (2 + -2x) = 4(x + -2) + 3(x + -3)

Reorder the terms:
30 + 2 + 10x + -2x = 4(x + -2) + 3(x + -3)

Combine like terms: 30 + 2 = 32
32 + 10x + -2x = 4(x + -2) + 3(x + -3)

Combine like terms: 10x + -2x = 8x
32 + 8x = 4(x + -2) + 3(x + -3)

Reorder the terms:
32 + 8x = 4(-2 + x) + 3(x + -3)
32 + 8x = (-2 * 4 + x * 4) + 3(x + -3)
32 + 8x = (-8 + 4x) + 3(x + -3)

Reorder the terms:
32 + 8x = -8 + 4x + 3(-3 + x)
32 + 8x = -8 + 4x + (-3 * 3 + x * 3)
32 + 8x = -8 + 4x + (-9 + 3x)

Reorder the terms:
32 + 8x = -8 + -9 + 4x + 3x

Combine like terms: -8 + -9 = -17
32 + 8x = -17 + 4x + 3x

Combine like terms: 4x + 3x = 7x
32 + 8x = -17 + 7x

Solving
32 + 8x = -17 + 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.
32 + 8x + -7x = -17 + 7x + -7x

Combine like terms: 8x + -7x = 1x
32 + 1x = -17 + 7x + -7x

Combine like terms: 7x + -7x = 0
32 + 1x = -17 + 0
32 + 1x = -17

Add '-32' to each side of the equation.
32 + -32 + 1x = -17 + -32

Combine like terms: 32 + -32 = 0
0 + 1x = -17 + -32
1x = -17 + -32

Combine like terms: -17 + -32 = -49
1x = -49

Divide each side by '1'.
x = -49

Simplifying
x = -49

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