-4(p+2)+8=2p(p-1)-7p+15

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Solution for -4(p+2)+8=2p(p-1)-7p+15 equation:


Simplifying
-4(p + 2) + 8 = 2p(p + -1) + -7p + 15

Reorder the terms:
-4(2 + p) + 8 = 2p(p + -1) + -7p + 15
(2 * -4 + p * -4) + 8 = 2p(p + -1) + -7p + 15
(-8 + -4p) + 8 = 2p(p + -1) + -7p + 15

Reorder the terms:
-8 + 8 + -4p = 2p(p + -1) + -7p + 15

Combine like terms: -8 + 8 = 0
0 + -4p = 2p(p + -1) + -7p + 15
-4p = 2p(p + -1) + -7p + 15

Reorder the terms:
-4p = 2p(-1 + p) + -7p + 15
-4p = (-1 * 2p + p * 2p) + -7p + 15
-4p = (-2p + 2p2) + -7p + 15

Reorder the terms:
-4p = 15 + -2p + -7p + 2p2

Combine like terms: -2p + -7p = -9p
-4p = 15 + -9p + 2p2

Solving
-4p = 15 + -9p + 2p2

Solving for variable 'p'.

Reorder the terms:
-15 + -4p + 9p + -2p2 = 15 + -9p + 2p2 + -15 + 9p + -2p2

Combine like terms: -4p + 9p = 5p
-15 + 5p + -2p2 = 15 + -9p + 2p2 + -15 + 9p + -2p2

Reorder the terms:
-15 + 5p + -2p2 = 15 + -15 + -9p + 9p + 2p2 + -2p2

Combine like terms: 15 + -15 = 0
-15 + 5p + -2p2 = 0 + -9p + 9p + 2p2 + -2p2
-15 + 5p + -2p2 = -9p + 9p + 2p2 + -2p2

Combine like terms: -9p + 9p = 0
-15 + 5p + -2p2 = 0 + 2p2 + -2p2
-15 + 5p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-15 + 5p + -2p2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
7.5 + -2.5p + p2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + -2.5p + -7.5 + p2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + -2.5p + p2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -2.5p + p2 = 0 + -7.5
-2.5p + p2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
-2.5p + p2 = -7.5

The p term is -2.5p.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5p + 1.5625 + p2 = -7.5 + 1.5625

Reorder the terms:
1.5625 + -2.5p + p2 = -7.5 + 1.5625

Combine like terms: -7.5 + 1.5625 = -5.9375
1.5625 + -2.5p + p2 = -5.9375

Factor a perfect square on the left side:
(p + -1.25)(p + -1.25) = -5.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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