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

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


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

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

Reorder the terms:
-14 + 6x + 6(-3 + x) = -3(4 + -5x) + 5x + -2
-14 + 6x + (-3 * 6 + x * 6) = -3(4 + -5x) + 5x + -2
-14 + 6x + (-18 + 6x) = -3(4 + -5x) + 5x + -2

Reorder the terms:
-14 + -18 + 6x + 6x = -3(4 + -5x) + 5x + -2

Combine like terms: -14 + -18 = -32
-32 + 6x + 6x = -3(4 + -5x) + 5x + -2

Combine like terms: 6x + 6x = 12x
-32 + 12x = -3(4 + -5x) + 5x + -2
-32 + 12x = (4 * -3 + -5x * -3) + 5x + -2
-32 + 12x = (-12 + 15x) + 5x + -2

Reorder the terms:
-32 + 12x = -12 + -2 + 15x + 5x

Combine like terms: -12 + -2 = -14
-32 + 12x = -14 + 15x + 5x

Combine like terms: 15x + 5x = 20x
-32 + 12x = -14 + 20x

Solving
-32 + 12x = -14 + 20x

Solving for variable 'x'.

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

Add '-20x' to each side of the equation.
-32 + 12x + -20x = -14 + 20x + -20x

Combine like terms: 12x + -20x = -8x
-32 + -8x = -14 + 20x + -20x

Combine like terms: 20x + -20x = 0
-32 + -8x = -14 + 0
-32 + -8x = -14

Add '32' to each side of the equation.
-32 + 32 + -8x = -14 + 32

Combine like terms: -32 + 32 = 0
0 + -8x = -14 + 32
-8x = -14 + 32

Combine like terms: -14 + 32 = 18
-8x = 18

Divide each side by '-8'.
x = -2.25

Simplifying
x = -2.25

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