29-4p=-3-4p(p-8)

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Solution for 29-4p=-3-4p(p-8) equation:


Simplifying
29 + -4p = -3 + -4p(p + -8)

Reorder the terms:
29 + -4p = -3 + -4p(-8 + p)
29 + -4p = -3 + (-8 * -4p + p * -4p)
29 + -4p = -3 + (32p + -4p2)

Solving
29 + -4p = -3 + 32p + -4p2

Solving for variable 'p'.

Reorder the terms:
29 + 3 + -4p + -32p + 4p2 = -3 + 32p + -4p2 + 3 + -32p + 4p2

Combine like terms: 29 + 3 = 32
32 + -4p + -32p + 4p2 = -3 + 32p + -4p2 + 3 + -32p + 4p2

Combine like terms: -4p + -32p = -36p
32 + -36p + 4p2 = -3 + 32p + -4p2 + 3 + -32p + 4p2

Reorder the terms:
32 + -36p + 4p2 = -3 + 3 + 32p + -32p + -4p2 + 4p2

Combine like terms: -3 + 3 = 0
32 + -36p + 4p2 = 0 + 32p + -32p + -4p2 + 4p2
32 + -36p + 4p2 = 32p + -32p + -4p2 + 4p2

Combine like terms: 32p + -32p = 0
32 + -36p + 4p2 = 0 + -4p2 + 4p2
32 + -36p + 4p2 = -4p2 + 4p2

Combine like terms: -4p2 + 4p2 = 0
32 + -36p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -9p + p2) = 0

Factor a trinomial.
4((1 + -1p)(8 + -1p)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1p = 0

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

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

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

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

Simplifying
p = 1

Subproblem 2
Set the factor '(8 + -1p)' equal to zero and attempt to solve:

Simplifying
8 + -1p = 0

Solving
8 + -1p = 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 + -1p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1p = 0 + -8
-1p = 0 + -8

Combine like terms: 0 + -8 = -8
-1p = -8

Divide each side by '-1'.
p = 8

Simplifying
p = 8
Solution
p = {1, 8}

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