3(4p+7)+4(7p-7)=8(5p-4)+6(7p-3)+1

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Solution for 3(4p+7)+4(7p-7)=8(5p-4)+6(7p-3)+1 equation: 


Simplifying
3(4p + 7) + 4(7p + -7) = 8(5p + -4) + 6(7p + -3) + 1

Reorder the terms:
3(7 + 4p) + 4(7p + -7) = 8(5p + -4) + 6(7p + -3) + 1
(7 * 3 + 4p * 3) + 4(7p + -7) = 8(5p + -4) + 6(7p + -3) + 1
(21 + 12p) + 4(7p + -7) = 8(5p + -4) + 6(7p + -3) + 1

Reorder the terms:
21 + 12p + 4(-7 + 7p) = 8(5p + -4) + 6(7p + -3) + 1
21 + 12p + (-7 * 4 + 7p * 4) = 8(5p + -4) + 6(7p + -3) + 1
21 + 12p + (-28 + 28p) = 8(5p + -4) + 6(7p + -3) + 1

Reorder the terms:
21 + -28 + 12p + 28p = 8(5p + -4) + 6(7p + -3) + 1

Combine like terms: 21 + -28 = -7
-7 + 12p + 28p = 8(5p + -4) + 6(7p + -3) + 1

Combine like terms: 12p + 28p = 40p
-7 + 40p = 8(5p + -4) + 6(7p + -3) + 1

Reorder the terms:
-7 + 40p = 8(-4 + 5p) + 6(7p + -3) + 1
-7 + 40p = (-4 * 8 + 5p * 8) + 6(7p + -3) + 1
-7 + 40p = (-32 + 40p) + 6(7p + -3) + 1

Reorder the terms:
-7 + 40p = -32 + 40p + 6(-3 + 7p) + 1
-7 + 40p = -32 + 40p + (-3 * 6 + 7p * 6) + 1
-7 + 40p = -32 + 40p + (-18 + 42p) + 1

Reorder the terms:
-7 + 40p = -32 + -18 + 1 + 40p + 42p

Combine like terms: -32 + -18 = -50
-7 + 40p = -50 + 1 + 40p + 42p

Combine like terms: -50 + 1 = -49
-7 + 40p = -49 + 40p + 42p

Combine like terms: 40p + 42p = 82p
-7 + 40p = -49 + 82p

Solving
-7 + 40p = -49 + 82p

Solving for variable 'p'.

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

Add '-82p' to each side of the equation.
-7 + 40p + -82p = -49 + 82p + -82p

Combine like terms: 40p + -82p = -42p
-7 + -42p = -49 + 82p + -82p

Combine like terms: 82p + -82p = 0
-7 + -42p = -49 + 0
-7 + -42p = -49

Add '7' to each side of the equation.
-7 + 7 + -42p = -49 + 7

Combine like terms: -7 + 7 = 0
0 + -42p = -49 + 7
-42p = -49 + 7

Combine like terms: -49 + 7 = -42
-42p = -42

Divide each side by '-42'.
p = 1

Simplifying
p = 1

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