(10sp-6s^2p+13sp^2)-(5sp^2-2sp-13s^2p)=

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Solution for (10sp-6s^2p+13sp^2)-(5sp^2-2sp-13s^2p)= equation:


Simplifying
(10sp + -6s2p + 13sp2) + -1(5sp2 + -2sp + -13s2p) = 0

Remove parenthesis around (10ps + -6ps2 + 13p2s)
10ps + -6ps2 + 13p2s + -1(5sp2 + -2sp + -13s2p) = 0

Reorder the terms:
10ps + -6ps2 + 13p2s + -1(-2ps + -13ps2 + 5p2s) = 0
10ps + -6ps2 + 13p2s + (-2ps * -1 + -13ps2 * -1 + 5p2s * -1) = 0
10ps + -6ps2 + 13p2s + (2ps + 13ps2 + -5p2s) = 0

Reorder the terms:
10ps + 2ps + -6ps2 + 13ps2 + 13p2s + -5p2s = 0

Combine like terms: 10ps + 2ps = 12ps
12ps + -6ps2 + 13ps2 + 13p2s + -5p2s = 0

Combine like terms: -6ps2 + 13ps2 = 7ps2
12ps + 7ps2 + 13p2s + -5p2s = 0

Combine like terms: 13p2s + -5p2s = 8p2s
12ps + 7ps2 + 8p2s = 0

Solving
12ps + 7ps2 + 8p2s = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'ps'.
ps(12 + 7s + 8p) = 0

Subproblem 1

Set the factor 'ps' equal to zero and attempt to solve: Simplifying ps = 0 Solving ps = 0 Move all terms containing p to the left, all other terms to the right. Simplifying ps = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(12 + 7s + 8p)' equal to zero and attempt to solve: Simplifying 12 + 7s + 8p = 0 Reorder the terms: 12 + 8p + 7s = 0 Solving 12 + 8p + 7s = 0 Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 8p + -12 + 7s = 0 + -12 Reorder the terms: 12 + -12 + 8p + 7s = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 8p + 7s = 0 + -12 8p + 7s = 0 + -12 Combine like terms: 0 + -12 = -12 8p + 7s = -12 Add '-7s' to each side of the equation. 8p + 7s + -7s = -12 + -7s Combine like terms: 7s + -7s = 0 8p + 0 = -12 + -7s 8p = -12 + -7s Divide each side by '8'. p = -1.5 + -0.875s Simplifying p = -1.5 + -0.875s

Solution

p = {-1.5 + -0.875s}

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