(p+4)(p+4)=7(p+4)-12

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Solution for (p+4)(p+4)=7(p+4)-12 equation: 


Simplifying
(p + 4)(p + 4) = 7(p + 4) + -12

Reorder the terms:
(4 + p)(p + 4) = 7(p + 4) + -12

Reorder the terms:
(4 + p)(4 + p) = 7(p + 4) + -12

Multiply (4 + p) * (4 + p)
(4(4 + p) + p(4 + p)) = 7(p + 4) + -12
((4 * 4 + p * 4) + p(4 + p)) = 7(p + 4) + -12
((16 + 4p) + p(4 + p)) = 7(p + 4) + -12
(16 + 4p + (4 * p + p * p)) = 7(p + 4) + -12
(16 + 4p + (4p + p2)) = 7(p + 4) + -12

Combine like terms: 4p + 4p = 8p
(16 + 8p + p2) = 7(p + 4) + -12

Reorder the terms:
16 + 8p + p2 = 7(4 + p) + -12
16 + 8p + p2 = (4 * 7 + p * 7) + -12
16 + 8p + p2 = (28 + 7p) + -12

Reorder the terms:
16 + 8p + p2 = 28 + -12 + 7p

Combine like terms: 28 + -12 = 16
16 + 8p + p2 = 16 + 7p

Add '-16' to each side of the equation.
16 + 8p + -16 + p2 = 16 + -16 + 7p

Reorder the terms:
16 + -16 + 8p + p2 = 16 + -16 + 7p

Combine like terms: 16 + -16 = 0
0 + 8p + p2 = 16 + -16 + 7p
8p + p2 = 16 + -16 + 7p

Combine like terms: 16 + -16 = 0
8p + p2 = 0 + 7p
8p + p2 = 7p

Solving
8p + p2 = 7p

Solving for variable 'p'.

Reorder the terms:
8p + -7p + p2 = 7p + -7p

Combine like terms: 8p + -7p = 1p
1p + p2 = 7p + -7p

Combine like terms: 7p + -7p = 0
1p + p2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(1 + p) = 0


Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0

Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 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 + p = 0 + -1

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

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

Simplifying
p = -1
Solution
p = {0, -1}

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