(7p-2)(7p-2)=5(7p-2)+6

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Solution for (7p-2)(7p-2)=5(7p-2)+6 equation: 


Simplifying
(7p + -2)(7p + -2) = 5(7p + -2) + 6

Reorder the terms:
(-2 + 7p)(7p + -2) = 5(7p + -2) + 6

Reorder the terms:
(-2 + 7p)(-2 + 7p) = 5(7p + -2) + 6

Multiply (-2 + 7p) * (-2 + 7p)
(-2(-2 + 7p) + 7p * (-2 + 7p)) = 5(7p + -2) + 6
((-2 * -2 + 7p * -2) + 7p * (-2 + 7p)) = 5(7p + -2) + 6
((4 + -14p) + 7p * (-2 + 7p)) = 5(7p + -2) + 6
(4 + -14p + (-2 * 7p + 7p * 7p)) = 5(7p + -2) + 6
(4 + -14p + (-14p + 49p2)) = 5(7p + -2) + 6

Combine like terms: -14p + -14p = -28p
(4 + -28p + 49p2) = 5(7p + -2) + 6

Reorder the terms:
4 + -28p + 49p2 = 5(-2 + 7p) + 6
4 + -28p + 49p2 = (-2 * 5 + 7p * 5) + 6
4 + -28p + 49p2 = (-10 + 35p) + 6

Reorder the terms:
4 + -28p + 49p2 = -10 + 6 + 35p

Combine like terms: -10 + 6 = -4
4 + -28p + 49p2 = -4 + 35p

Solving
4 + -28p + 49p2 = -4 + 35p

Solving for variable 'p'.

Reorder the terms:
4 + 4 + -28p + -35p + 49p2 = -4 + 35p + 4 + -35p

Combine like terms: 4 + 4 = 8
8 + -28p + -35p + 49p2 = -4 + 35p + 4 + -35p

Combine like terms: -28p + -35p = -63p
8 + -63p + 49p2 = -4 + 35p + 4 + -35p

Reorder the terms:
8 + -63p + 49p2 = -4 + 4 + 35p + -35p

Combine like terms: -4 + 4 = 0
8 + -63p + 49p2 = 0 + 35p + -35p
8 + -63p + 49p2 = 35p + -35p

Combine like terms: 35p + -35p = 0
8 + -63p + 49p2 = 0

Factor a trinomial.
(1 + -7p)(8 + -7p) = 0


Subproblem 1
Set the factor '(1 + -7p)' equal to zero and attempt to solve:

Simplifying
1 + -7p = 0

Solving
1 + -7p = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7p = 0 + -1
-7p = 0 + -1

Combine like terms: 0 + -1 = -1
-7p = -1

Divide each side by '-7'.
p = 0.1428571429

Simplifying
p = 0.1428571429

Subproblem 2
Set the factor '(8 + -7p)' equal to zero and attempt to solve:

Simplifying
8 + -7p = 0

Solving
8 + -7p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7p = 0 + -8
-7p = 0 + -8

Combine like terms: 0 + -8 = -8
-7p = -8

Divide each side by '-7'.
p = 1.142857143

Simplifying
p = 1.142857143
Solution
p = {0.1428571429, 1.142857143}

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