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Simplifying 0 = 8a2 + 3a(a + 2b + 4c) + -2a(5a + 6b + 5c) 0 = 8a2 + (a * 3a + 2b * 3a + 4c * 3a) + -2a(5a + 6b + 5c) Reorder the terms: 0 = 8a2 + (6ab + 12ac + 3a2) + -2a(5a + 6b + 5c) 0 = 8a2 + (6ab + 12ac + 3a2) + -2a(5a + 6b + 5c) 0 = 8a2 + 6ab + 12ac + 3a2 + (5a * -2a + 6b * -2a + 5c * -2a) Reorder the terms: 0 = 8a2 + 6ab + 12ac + 3a2 + (-12ab + -10ac + -10a2) 0 = 8a2 + 6ab + 12ac + 3a2 + (-12ab + -10ac + -10a2) Reorder the terms: 0 = 6ab + -12ab + 12ac + -10ac + 8a2 + 3a2 + -10a2 Combine like terms: 6ab + -12ab = -6ab 0 = -6ab + 12ac + -10ac + 8a2 + 3a2 + -10a2 Combine like terms: 12ac + -10ac = 2ac 0 = -6ab + 2ac + 8a2 + 3a2 + -10a2 Combine like terms: 8a2 + 3a2 = 11a2 0 = -6ab + 2ac + 11a2 + -10a2 Combine like terms: 11a2 + -10a2 = 1a2 0 = -6ab + 2ac + 1a2 Solving 0 = -6ab + 2ac + 1a2 Solving for variable 'a'. Remove the zero: 6ab + -2ac + -1a2 = -6ab + 2ac + 1a2 + 6ab + -2ac + -1a2 Reorder the terms: 6ab + -2ac + -1a2 = -6ab + 6ab + 2ac + -2ac + 1a2 + -1a2 Combine like terms: -6ab + 6ab = 0 6ab + -2ac + -1a2 = 0 + 2ac + -2ac + 1a2 + -1a2 6ab + -2ac + -1a2 = 2ac + -2ac + 1a2 + -1a2 Combine like terms: 2ac + -2ac = 0 6ab + -2ac + -1a2 = 0 + 1a2 + -1a2 6ab + -2ac + -1a2 = 1a2 + -1a2 Combine like terms: 1a2 + -1a2 = 0 6ab + -2ac + -1a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(6b + -2c + -1a) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(6b + -2c + -1a)' equal to zero and attempt to solve: Simplifying 6b + -2c + -1a = 0 Reorder the terms: -1a + 6b + -2c = 0 Solving -1a + 6b + -2c = 0 Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. -1a + 6b + -6b + -2c = 0 + -6b Combine like terms: 6b + -6b = 0 -1a + 0 + -2c = 0 + -6b -1a + -2c = 0 + -6b Remove the zero: -1a + -2c = -6b Add '2c' to each side of the equation. -1a + -2c + 2c = -6b + 2c Combine like terms: -2c + 2c = 0 -1a + 0 = -6b + 2c -1a = -6b + 2c Divide each side by '-1'. a = 6b + -2c Simplifying a = 6b + -2cSolution
a = {0, 6b + -2c}
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