5(t-2)-3(4-t)=2(t+3)-40

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Solution for 5(t-2)-3(4-t)=2(t+3)-40 equation:


Simplifying
5(t + -2) + -3(4 + -1t) = 2(t + 3) + -40

Reorder the terms:
5(-2 + t) + -3(4 + -1t) = 2(t + 3) + -40
(-2 * 5 + t * 5) + -3(4 + -1t) = 2(t + 3) + -40
(-10 + 5t) + -3(4 + -1t) = 2(t + 3) + -40
-10 + 5t + (4 * -3 + -1t * -3) = 2(t + 3) + -40
-10 + 5t + (-12 + 3t) = 2(t + 3) + -40

Reorder the terms:
-10 + -12 + 5t + 3t = 2(t + 3) + -40

Combine like terms: -10 + -12 = -22
-22 + 5t + 3t = 2(t + 3) + -40

Combine like terms: 5t + 3t = 8t
-22 + 8t = 2(t + 3) + -40

Reorder the terms:
-22 + 8t = 2(3 + t) + -40
-22 + 8t = (3 * 2 + t * 2) + -40
-22 + 8t = (6 + 2t) + -40

Reorder the terms:
-22 + 8t = 6 + -40 + 2t

Combine like terms: 6 + -40 = -34
-22 + 8t = -34 + 2t

Solving
-22 + 8t = -34 + 2t

Solving for variable 't'.

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

Add '-2t' to each side of the equation.
-22 + 8t + -2t = -34 + 2t + -2t

Combine like terms: 8t + -2t = 6t
-22 + 6t = -34 + 2t + -2t

Combine like terms: 2t + -2t = 0
-22 + 6t = -34 + 0
-22 + 6t = -34

Add '22' to each side of the equation.
-22 + 22 + 6t = -34 + 22

Combine like terms: -22 + 22 = 0
0 + 6t = -34 + 22
6t = -34 + 22

Combine like terms: -34 + 22 = -12
6t = -12

Divide each side by '6'.
t = -2

Simplifying
t = -2

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