(-5p-1)(-5p-1)=17(-5p-1)-72

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Solution for (-5p-1)(-5p-1)=17(-5p-1)-72 equation:


Simplifying
(-5p + -1)(-5p + -1) = 17(-5p + -1) + -72

Reorder the terms:
(-1 + -5p)(-5p + -1) = 17(-5p + -1) + -72

Reorder the terms:
(-1 + -5p)(-1 + -5p) = 17(-5p + -1) + -72

Multiply (-1 + -5p) * (-1 + -5p)
(-1(-1 + -5p) + -5p * (-1 + -5p)) = 17(-5p + -1) + -72
((-1 * -1 + -5p * -1) + -5p * (-1 + -5p)) = 17(-5p + -1) + -72
((1 + 5p) + -5p * (-1 + -5p)) = 17(-5p + -1) + -72
(1 + 5p + (-1 * -5p + -5p * -5p)) = 17(-5p + -1) + -72
(1 + 5p + (5p + 25p2)) = 17(-5p + -1) + -72

Combine like terms: 5p + 5p = 10p
(1 + 10p + 25p2) = 17(-5p + -1) + -72

Reorder the terms:
1 + 10p + 25p2 = 17(-1 + -5p) + -72
1 + 10p + 25p2 = (-1 * 17 + -5p * 17) + -72
1 + 10p + 25p2 = (-17 + -85p) + -72

Reorder the terms:
1 + 10p + 25p2 = -17 + -72 + -85p

Combine like terms: -17 + -72 = -89
1 + 10p + 25p2 = -89 + -85p

Solving
1 + 10p + 25p2 = -89 + -85p

Solving for variable 'p'.

Reorder the terms:
1 + 89 + 10p + 85p + 25p2 = -89 + -85p + 89 + 85p

Combine like terms: 1 + 89 = 90
90 + 10p + 85p + 25p2 = -89 + -85p + 89 + 85p

Combine like terms: 10p + 85p = 95p
90 + 95p + 25p2 = -89 + -85p + 89 + 85p

Reorder the terms:
90 + 95p + 25p2 = -89 + 89 + -85p + 85p

Combine like terms: -89 + 89 = 0
90 + 95p + 25p2 = 0 + -85p + 85p
90 + 95p + 25p2 = -85p + 85p

Combine like terms: -85p + 85p = 0
90 + 95p + 25p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + 19p + 5p2) = 0

Factor a trinomial.
5((2 + p)(9 + 5p)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(2 + p)' equal to zero and attempt to solve: Simplifying 2 + p = 0 Solving 2 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0 + -2 p = 0 + -2 Combine like terms: 0 + -2 = -2 p = -2 Simplifying p = -2

Subproblem 2

Set the factor '(9 + 5p)' equal to zero and attempt to solve: Simplifying 9 + 5p = 0 Solving 9 + 5p = 0 Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5p = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5p = 0 + -9 5p = 0 + -9 Combine like terms: 0 + -9 = -9 5p = -9 Divide each side by '5'. p = -1.8 Simplifying p = -1.8

Solution

p = {-2, -1.8}

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