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Simplifying 2(p + -1g[2p + -1r(2p + 1) + 3pr] + -2r) = 0 Reorder the terms: 2(p + -1g[2p + -1r(1 + 2p) + 3pr] + -2r) = 0 2(p + -1g[2p + (1 * -1r + 2p * -1r) + 3pr] + -2r) = 0 Reorder the terms: 2(p + -1g[2p + (-2pr + -1r) + 3pr] + -2r) = 0 2(p + -1g[2p + (-2pr + -1r) + 3pr] + -2r) = 0 Reorder the terms: 2(p + -1g[2p + -2pr + 3pr + -1r] + -2r) = 0 Combine like terms: -2pr + 3pr = 1pr 2(p + -1g[2p + 1pr + -1r] + -2r) = 0 2(p + [2p * -1g + 1pr * -1g + -1r * -1g] + -2r) = 0 2(p + [-2gp + -1gpr + 1gr] + -2r) = 0 Reorder the terms: 2(-2gp + -1gpr + 1gr + p + -2r) = 0 (-2gp * 2 + -1gpr * 2 + 1gr * 2 + p * 2 + -2r * 2) = 0 (-4gp + -2gpr + 2gr + 2p + -4r) = 0 Solving -4gp + -2gpr + 2gr + 2p + -4r = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2p' to each side of the equation. -4gp + -2gpr + 2gr + 2p + -2p + -4r = 0 + -2p Combine like terms: 2p + -2p = 0 -4gp + -2gpr + 2gr + 0 + -4r = 0 + -2p -4gp + -2gpr + 2gr + -4r = 0 + -2p Remove the zero: -4gp + -2gpr + 2gr + -4r = -2p Add '4r' to each side of the equation. -4gp + -2gpr + 2gr + -4r + 4r = -2p + 4r Combine like terms: -4r + 4r = 0 -4gp + -2gpr + 2gr + 0 = -2p + 4r -4gp + -2gpr + 2gr = -2p + 4r Reorder the terms: -4gp + -2gpr + 2gr + 2p + -4r = -2p + 2p + 4r + -4r Combine like terms: -2p + 2p = 0 -4gp + -2gpr + 2gr + 2p + -4r = 0 + 4r + -4r -4gp + -2gpr + 2gr + 2p + -4r = 4r + -4r Combine like terms: 4r + -4r = 0 -4gp + -2gpr + 2gr + 2p + -4r = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2gp + -1gpr + gr + p + -2r) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2gp + -1gpr + gr + p + -2r)' equal to zero and attempt to solve: Simplifying -2gp + -1gpr + gr + p + -2r = 0 Solving -2gp + -1gpr + gr + p + -2r = 0 Move all terms containing g to the left, all other terms to the right. Add '-1p' to each side of the equation. -2gp + -1gpr + gr + p + -1p + -2r = 0 + -1p Combine like terms: p + -1p = 0 -2gp + -1gpr + gr + 0 + -2r = 0 + -1p -2gp + -1gpr + gr + -2r = 0 + -1p Remove the zero: -2gp + -1gpr + gr + -2r = -1p Add '2r' to each side of the equation. -2gp + -1gpr + gr + -2r + 2r = -1p + 2r Combine like terms: -2r + 2r = 0 -2gp + -1gpr + gr + 0 = -1p + 2r -2gp + -1gpr + gr = -1p + 2r 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.
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