-(t-7)+4(7-t)=6(t-2)-3(3-t)

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


Simplifying
-1(t + -7) + 4(7 + -1t) = 6(t + -2) + -3(3 + -1t)

Reorder the terms:
-1(-7 + t) + 4(7 + -1t) = 6(t + -2) + -3(3 + -1t)
(-7 * -1 + t * -1) + 4(7 + -1t) = 6(t + -2) + -3(3 + -1t)
(7 + -1t) + 4(7 + -1t) = 6(t + -2) + -3(3 + -1t)
7 + -1t + (7 * 4 + -1t * 4) = 6(t + -2) + -3(3 + -1t)
7 + -1t + (28 + -4t) = 6(t + -2) + -3(3 + -1t)

Reorder the terms:
7 + 28 + -1t + -4t = 6(t + -2) + -3(3 + -1t)

Combine like terms: 7 + 28 = 35
35 + -1t + -4t = 6(t + -2) + -3(3 + -1t)

Combine like terms: -1t + -4t = -5t
35 + -5t = 6(t + -2) + -3(3 + -1t)

Reorder the terms:
35 + -5t = 6(-2 + t) + -3(3 + -1t)
35 + -5t = (-2 * 6 + t * 6) + -3(3 + -1t)
35 + -5t = (-12 + 6t) + -3(3 + -1t)
35 + -5t = -12 + 6t + (3 * -3 + -1t * -3)
35 + -5t = -12 + 6t + (-9 + 3t)

Reorder the terms:
35 + -5t = -12 + -9 + 6t + 3t

Combine like terms: -12 + -9 = -21
35 + -5t = -21 + 6t + 3t

Combine like terms: 6t + 3t = 9t
35 + -5t = -21 + 9t

Solving
35 + -5t = -21 + 9t

Solving for variable 't'.

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

Add '-9t' to each side of the equation.
35 + -5t + -9t = -21 + 9t + -9t

Combine like terms: -5t + -9t = -14t
35 + -14t = -21 + 9t + -9t

Combine like terms: 9t + -9t = 0
35 + -14t = -21 + 0
35 + -14t = -21

Add '-35' to each side of the equation.
35 + -35 + -14t = -21 + -35

Combine like terms: 35 + -35 = 0
0 + -14t = -21 + -35
-14t = -21 + -35

Combine like terms: -21 + -35 = -56
-14t = -56

Divide each side by '-14'.
t = 4

Simplifying
t = 4

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