6(x-7)-7(x-6)=x+6(x-6)

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Solution for 6(x-7)-7(x-6)=x+6(x-6) equation:


Simplifying
6(x + -7) + -7(x + -6) = x + 6(x + -6)

Reorder the terms:
6(-7 + x) + -7(x + -6) = x + 6(x + -6)
(-7 * 6 + x * 6) + -7(x + -6) = x + 6(x + -6)
(-42 + 6x) + -7(x + -6) = x + 6(x + -6)

Reorder the terms:
-42 + 6x + -7(-6 + x) = x + 6(x + -6)
-42 + 6x + (-6 * -7 + x * -7) = x + 6(x + -6)
-42 + 6x + (42 + -7x) = x + 6(x + -6)

Reorder the terms:
-42 + 42 + 6x + -7x = x + 6(x + -6)

Combine like terms: -42 + 42 = 0
0 + 6x + -7x = x + 6(x + -6)
6x + -7x = x + 6(x + -6)

Combine like terms: 6x + -7x = -1x
-1x = x + 6(x + -6)

Reorder the terms:
-1x = x + 6(-6 + x)
-1x = x + (-6 * 6 + x * 6)
-1x = x + (-36 + 6x)

Reorder the terms:
-1x = -36 + x + 6x

Combine like terms: x + 6x = 7x
-1x = -36 + 7x

Solving
-1x = -36 + 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.
-1x + -7x = -36 + 7x + -7x

Combine like terms: -1x + -7x = -8x
-8x = -36 + 7x + -7x

Combine like terms: 7x + -7x = 0
-8x = -36 + 0
-8x = -36

Divide each side by '-8'.
x = 4.5

Simplifying
x = 4.5

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