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

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


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

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

Reorder the terms:
-6 + 2x + 3(-5 + x) = 4(x + -2)
-6 + 2x + (-5 * 3 + x * 3) = 4(x + -2)
-6 + 2x + (-15 + 3x) = 4(x + -2)

Reorder the terms:
-6 + -15 + 2x + 3x = 4(x + -2)

Combine like terms: -6 + -15 = -21
-21 + 2x + 3x = 4(x + -2)

Combine like terms: 2x + 3x = 5x
-21 + 5x = 4(x + -2)

Reorder the terms:
-21 + 5x = 4(-2 + x)
-21 + 5x = (-2 * 4 + x * 4)
-21 + 5x = (-8 + 4x)

Solving
-21 + 5x = -8 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
-21 + 5x + -4x = -8 + 4x + -4x

Combine like terms: 5x + -4x = 1x
-21 + 1x = -8 + 4x + -4x

Combine like terms: 4x + -4x = 0
-21 + 1x = -8 + 0
-21 + 1x = -8

Add '21' to each side of the equation.
-21 + 21 + 1x = -8 + 21

Combine like terms: -21 + 21 = 0
0 + 1x = -8 + 21
1x = -8 + 21

Combine like terms: -8 + 21 = 13
1x = 13

Divide each side by '1'.
x = 13

Simplifying
x = 13

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