-3(3p+6)-2(6-14p)=3p(1+6p)

Solution for -3(3p+6)-2(6-14p)=3p(1+6p) equation:

Simplifying
-3(3p + 6) + -2(6 + -14p) = 3p(1 + 6p)

Reorder the terms:
-3(6 + 3p) + -2(6 + -14p) = 3p(1 + 6p)
(6 * -3 + 3p * -3) + -2(6 + -14p) = 3p(1 + 6p)
(-18 + -9p) + -2(6 + -14p) = 3p(1 + 6p)
-18 + -9p + (6 * -2 + -14p * -2) = 3p(1 + 6p)
-18 + -9p + (-12 + 28p) = 3p(1 + 6p)

Reorder the terms:
-18 + -12 + -9p + 28p = 3p(1 + 6p)

Combine like terms: -18 + -12 = -30
-30 + -9p + 28p = 3p(1 + 6p)

Combine like terms: -9p + 28p = 19p
-30 + 19p = 3p(1 + 6p)
-30 + 19p = (1 * 3p + 6p * 3p)
-30 + 19p = (3p + 18p2)

Solving
-30 + 19p = 3p + 18p2

Solving for variable 'p'.

Combine like terms: 19p + -3p = 16p
-30 + 16p + -18p2 = 3p + 18p2 + -3p + -18p2

Reorder the terms:
-30 + 16p + -18p2 = 3p + -3p + 18p2 + -18p2

Combine like terms: 3p + -3p = 0
-30 + 16p + -18p2 = 0 + 18p2 + -18p2
-30 + 16p + -18p2 = 18p2 + -18p2

Combine like terms: 18p2 + -18p2 = 0
-30 + 16p + -18p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 8p + -9p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 8p + -9p2)' equal to zero and attempt to solve:

Simplifying
-15 + 8p + -9p2 = 0

Solving
-15 + 8p + -9p2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
1.666666667 + -0.8888888889p + p2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -0.8888888889p + -1.666666667 + p2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -0.8888888889p + p2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -0.8888888889p + p2 = 0 + -1.666666667
-0.8888888889p + p2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-0.8888888889p + p2 = -1.666666667

The p term is -0.8888888889p.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889p + 0.1975308642 + p2 = -1.666666667 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889p + p2 = -1.666666667 + 0.1975308642

Combine like terms: -1.666666667 + 0.1975308642 = -1.4691358028
0.1975308642 + -0.8888888889p + p2 = -1.4691358028

Factor a perfect square on the left side:
(p + -0.4444444445)(p + -0.4444444445) = -1.4691358028

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.