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Simplifying (ax + 7)(ax + 5) = (2a + 7)(2a + 5) Reorder the terms: (7 + ax)(ax + 5) = (2a + 7)(2a + 5) Reorder the terms: (7 + ax)(5 + ax) = (2a + 7)(2a + 5) Multiply (7 + ax) * (5 + ax) (7(5 + ax) + ax(5 + ax)) = (2a + 7)(2a + 5) ((5 * 7 + ax * 7) + ax(5 + ax)) = (2a + 7)(2a + 5) ((35 + 7ax) + ax(5 + ax)) = (2a + 7)(2a + 5) (35 + 7ax + (5 * ax + ax * ax)) = (2a + 7)(2a + 5) (35 + 7ax + (5ax + a2x2)) = (2a + 7)(2a + 5) Combine like terms: 7ax + 5ax = 12ax (35 + 12ax + a2x2) = (2a + 7)(2a + 5) Reorder the terms: 35 + 12ax + a2x2 = (7 + 2a)(2a + 5) Reorder the terms: 35 + 12ax + a2x2 = (7 + 2a)(5 + 2a) Multiply (7 + 2a) * (5 + 2a) 35 + 12ax + a2x2 = (7(5 + 2a) + 2a * (5 + 2a)) 35 + 12ax + a2x2 = ((5 * 7 + 2a * 7) + 2a * (5 + 2a)) 35 + 12ax + a2x2 = ((35 + 14a) + 2a * (5 + 2a)) 35 + 12ax + a2x2 = (35 + 14a + (5 * 2a + 2a * 2a)) 35 + 12ax + a2x2 = (35 + 14a + (10a + 4a2)) Combine like terms: 14a + 10a = 24a 35 + 12ax + a2x2 = (35 + 24a + 4a2) Add '-35' to each side of the equation. 35 + 12ax + -35 + a2x2 = 35 + 24a + -35 + 4a2 Reorder the terms: 35 + -35 + 12ax + a2x2 = 35 + 24a + -35 + 4a2 Combine like terms: 35 + -35 = 0 0 + 12ax + a2x2 = 35 + 24a + -35 + 4a2 12ax + a2x2 = 35 + 24a + -35 + 4a2 Reorder the terms: 12ax + a2x2 = 35 + -35 + 24a + 4a2 Combine like terms: 35 + -35 = 0 12ax + a2x2 = 0 + 24a + 4a2 12ax + a2x2 = 24a + 4a2 Solving 12ax + a2x2 = 24a + 4a2 Solving for variable 'a'. Reorder the terms: -24a + 12ax + -4a2 + a2x2 = 24a + 4a2 + -24a + -4a2 Reorder the terms: -24a + 12ax + -4a2 + a2x2 = 24a + -24a + 4a2 + -4a2 Combine like terms: 24a + -24a = 0 -24a + 12ax + -4a2 + a2x2 = 0 + 4a2 + -4a2 -24a + 12ax + -4a2 + a2x2 = 4a2 + -4a2 Combine like terms: 4a2 + -4a2 = 0 -24a + 12ax + -4a2 + a2x2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-24 + 12x + -4a + ax2) = 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 '(-24 + 12x + -4a + ax2)' equal to zero and attempt to solve: Simplifying -24 + 12x + -4a + ax2 = 0 Reorder the terms: -24 + -4a + ax2 + 12x = 0 Solving -24 + -4a + ax2 + 12x = 0 Move all terms containing a to the left, all other terms to the right. Add '24' to each side of the equation. -24 + -4a + ax2 + 24 + 12x = 0 + 24 Reorder the terms: -24 + 24 + -4a + ax2 + 12x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4a + ax2 + 12x = 0 + 24 -4a + ax2 + 12x = 0 + 24 Combine like terms: 0 + 24 = 24 -4a + ax2 + 12x = 24 Add '-12x' to each side of the equation. -4a + ax2 + 12x + -12x = 24 + -12x Combine like terms: 12x + -12x = 0 -4a + ax2 + 0 = 24 + -12x -4a + ax2 = 24 + -12x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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