2(3+p)6(-4p)=6(1)3(-p+7)

Solution for 2(3+p)6(-4p)=6(1)3(-p+7) equation:

Simplifying
2(3 + p) * 6(-4p) = 6(1) * 3(-1p + 7)

Remove parenthesis around (-4p)
2(3 + p) * 6 * -4p = 6(1) * 3(-1p + 7)

Reorder the terms for easier multiplication:
2 * 6 * -4p(3 + p) = 6(1) * 3(-1p + 7)

Multiply 2 * 6
12 * -4p(3 + p) = 6(1) * 3(-1p + 7)

Multiply 12 * -4
-48p(3 + p) = 6(1) * 3(-1p + 7)
(3 * -48p + p * -48p) = 6(1) * 3(-1p + 7)
(-144p + -48p2) = 6(1) * 3(-1p + 7)

Reorder the terms:
-144p + -48p2 = 6 * 1 * 3(7 + -1p)

Multiply 6 * 1
-144p + -48p2 = 6 * 3(7 + -1p)

Multiply 6 * 3
-144p + -48p2 = 18(7 + -1p)
-144p + -48p2 = (7 * 18 + -1p * 18)
-144p + -48p2 = (126 + -18p)

Solving
-144p + -48p2 = 126 + -18p

Solving for variable 'p'.

Reorder the terms:
-126 + -144p + 18p + -48p2 = 126 + -18p + -126 + 18p

Combine like terms: -144p + 18p = -126p
-126 + -126p + -48p2 = 126 + -18p + -126 + 18p

Reorder the terms:
-126 + -126p + -48p2 = 126 + -126 + -18p + 18p

Combine like terms: 126 + -126 = 0
-126 + -126p + -48p2 = 0 + -18p + 18p
-126 + -126p + -48p2 = -18p + 18p

Combine like terms: -18p + 18p = 0
-126 + -126p + -48p2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(21 + 21p + 8p2) = 0

Ignore the factor -6.
Subproblem 1
Set the factor '(21 + 21p + 8p2)' equal to zero and attempt to solve:

Simplifying
21 + 21p + 8p2 = 0

Solving
21 + 21p + 8p2 = 0

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

Divide each side by '8'.
2.625 + 2.625p + p2 = 0

Move the constant term to the right:

Add '-2.625' to each side of the equation.
2.625 + 2.625p + -2.625 + p2 = 0 + -2.625

Reorder the terms:
2.625 + -2.625 + 2.625p + p2 = 0 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + 2.625p + p2 = 0 + -2.625
2.625p + p2 = 0 + -2.625

Combine like terms: 0 + -2.625 = -2.625
2.625p + p2 = -2.625

The p term is 2.625p.  Take half its coefficient (1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
2.625p + 1.72265625 + p2 = -2.625 + 1.72265625

Reorder the terms:
1.72265625 + 2.625p + p2 = -2.625 + 1.72265625

Combine like terms: -2.625 + 1.72265625 = -0.90234375
1.72265625 + 2.625p + p2 = -0.90234375

Factor a perfect square on the left side:
(p + 1.3125)(p + 1.3125) = -0.90234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.