(-9p)(-10+3p)=7p(-9+3p)

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Solution for (-9p)(-10+3p)=7p(-9+3p) equation: 


Simplifying
(-9p)(-10 + 3p) = 7p(-9 + 3p)

Remove parenthesis around (-9p)
-9p(-10 + 3p) = 7p(-9 + 3p)
(-10 * -9p + 3p * -9p) = 7p(-9 + 3p)
(90p + -27p2) = 7p(-9 + 3p)
90p + -27p2 = (-9 * 7p + 3p * 7p)
90p + -27p2 = (-63p + 21p2)

Solving
90p + -27p2 = -63p + 21p2

Solving for variable 'p'.

Reorder the terms:
90p + 63p + -27p2 + -21p2 = -63p + 21p2 + 63p + -21p2

Combine like terms: 90p + 63p = 153p
153p + -27p2 + -21p2 = -63p + 21p2 + 63p + -21p2

Combine like terms: -27p2 + -21p2 = -48p2
153p + -48p2 = -63p + 21p2 + 63p + -21p2

Reorder the terms:
153p + -48p2 = -63p + 63p + 21p2 + -21p2

Combine like terms: -63p + 63p = 0
153p + -48p2 = 0 + 21p2 + -21p2
153p + -48p2 = 21p2 + -21p2

Combine like terms: 21p2 + -21p2 = 0
153p + -48p2 = 0

Factor out the Greatest Common Factor (GCF), '3p'.
3p(51 + -16p) = 0

Ignore the factor 3.

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 '(51 + -16p)' equal to zero and attempt to solve:

Simplifying
51 + -16p = 0

Solving
51 + -16p = 0

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

Add '-51' to each side of the equation.
51 + -51 + -16p = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -16p = 0 + -51
-16p = 0 + -51

Combine like terms: 0 + -51 = -51
-16p = -51

Divide each side by '-16'.
p = 3.1875

Simplifying
p = 3.1875
Solution
p = {0, 3.1875}

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