7(x+4)+6(x-3)=8(x-3)-2(x+4)

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Solution for 7(x+4)+6(x-3)=8(x-3)-2(x+4) equation: 


Simplifying
7(x + 4) + 6(x + -3) = 8(x + -3) + -2(x + 4)

Reorder the terms:
7(4 + x) + 6(x + -3) = 8(x + -3) + -2(x + 4)
(4 * 7 + x * 7) + 6(x + -3) = 8(x + -3) + -2(x + 4)
(28 + 7x) + 6(x + -3) = 8(x + -3) + -2(x + 4)

Reorder the terms:
28 + 7x + 6(-3 + x) = 8(x + -3) + -2(x + 4)
28 + 7x + (-3 * 6 + x * 6) = 8(x + -3) + -2(x + 4)
28 + 7x + (-18 + 6x) = 8(x + -3) + -2(x + 4)

Reorder the terms:
28 + -18 + 7x + 6x = 8(x + -3) + -2(x + 4)

Combine like terms: 28 + -18 = 10
10 + 7x + 6x = 8(x + -3) + -2(x + 4)

Combine like terms: 7x + 6x = 13x
10 + 13x = 8(x + -3) + -2(x + 4)

Reorder the terms:
10 + 13x = 8(-3 + x) + -2(x + 4)
10 + 13x = (-3 * 8 + x * 8) + -2(x + 4)
10 + 13x = (-24 + 8x) + -2(x + 4)

Reorder the terms:
10 + 13x = -24 + 8x + -2(4 + x)
10 + 13x = -24 + 8x + (4 * -2 + x * -2)
10 + 13x = -24 + 8x + (-8 + -2x)

Reorder the terms:
10 + 13x = -24 + -8 + 8x + -2x

Combine like terms: -24 + -8 = -32
10 + 13x = -32 + 8x + -2x

Combine like terms: 8x + -2x = 6x
10 + 13x = -32 + 6x

Solving
10 + 13x = -32 + 6x

Solving for variable 'x'.

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

Add '-6x' to each side of the equation.
10 + 13x + -6x = -32 + 6x + -6x

Combine like terms: 13x + -6x = 7x
10 + 7x = -32 + 6x + -6x

Combine like terms: 6x + -6x = 0
10 + 7x = -32 + 0
10 + 7x = -32

Add '-10' to each side of the equation.
10 + -10 + 7x = -32 + -10

Combine like terms: 10 + -10 = 0
0 + 7x = -32 + -10
7x = -32 + -10

Combine like terms: -32 + -10 = -42
7x = -42

Divide each side by '7'.
x = -6

Simplifying
x = -6

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