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Simplifying (ax + 3)(bx + 8) = 7x2 + cx + 24 Reorder the terms: (3 + ax)(bx + 8) = 7x2 + cx + 24 Reorder the terms: (3 + ax)(8 + bx) = 7x2 + cx + 24 Multiply (3 + ax) * (8 + bx) (3(8 + bx) + ax(8 + bx)) = 7x2 + cx + 24 ((8 * 3 + bx * 3) + ax(8 + bx)) = 7x2 + cx + 24 ((24 + 3bx) + ax(8 + bx)) = 7x2 + cx + 24 (24 + 3bx + (8 * ax + bx * ax)) = 7x2 + cx + 24 Reorder the terms: (24 + 3bx + (abx2 + 8ax)) = 7x2 + cx + 24 (24 + 3bx + (abx2 + 8ax)) = 7x2 + cx + 24 Reorder the terms: (24 + abx2 + 8ax + 3bx) = 7x2 + cx + 24 (24 + abx2 + 8ax + 3bx) = 7x2 + cx + 24 Reorder the terms: 24 + abx2 + 8ax + 3bx = 24 + cx + 7x2 Add '-24' to each side of the equation. 24 + abx2 + 8ax + -24 + 3bx = 24 + cx + -24 + 7x2 Reorder the terms: 24 + -24 + abx2 + 8ax + 3bx = 24 + cx + -24 + 7x2 Combine like terms: 24 + -24 = 0 0 + abx2 + 8ax + 3bx = 24 + cx + -24 + 7x2 abx2 + 8ax + 3bx = 24 + cx + -24 + 7x2 Reorder the terms: abx2 + 8ax + 3bx = 24 + -24 + cx + 7x2 Combine like terms: 24 + -24 = 0 abx2 + 8ax + 3bx = 0 + cx + 7x2 abx2 + 8ax + 3bx = cx + 7x2 Solving abx2 + 8ax + 3bx = cx + 7x2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3bx' to each side of the equation. abx2 + 8ax + 3bx + -3bx = cx + -3bx + 7x2 Combine like terms: 3bx + -3bx = 0 abx2 + 8ax + 0 = cx + -3bx + 7x2 abx2 + 8ax = cx + -3bx + 7x2 Reorder the terms: abx2 + 8ax = -3bx + cx + 7x2 Reorder the terms: abx2 + 8ax + 3bx + -1cx + -7x2 = -3bx + 3bx + cx + -1cx + 7x2 + -7x2 Combine like terms: -3bx + 3bx = 0 abx2 + 8ax + 3bx + -1cx + -7x2 = 0 + cx + -1cx + 7x2 + -7x2 abx2 + 8ax + 3bx + -1cx + -7x2 = cx + -1cx + 7x2 + -7x2 Combine like terms: cx + -1cx = 0 abx2 + 8ax + 3bx + -1cx + -7x2 = 0 + 7x2 + -7x2 abx2 + 8ax + 3bx + -1cx + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 abx2 + 8ax + 3bx + -1cx + -7x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(abx + 8a + 3b + -1c + -7x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(abx + 8a + 3b + -1c + -7x)' equal to zero and attempt to solve: Simplifying abx + 8a + 3b + -1c + -7x = 0 Reorder the terms: 8a + abx + 3b + -1c + -7x = 0 Solving 8a + abx + 3b + -1c + -7x = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 8a + abx + 3b + -1c + -3b + -7x = 0 + -3b Reorder the terms: 8a + abx + 3b + -3b + -1c + -7x = 0 + -3b Combine like terms: 3b + -3b = 0 8a + abx + 0 + -1c + -7x = 0 + -3b 8a + abx + -1c + -7x = 0 + -3b Remove the zero: 8a + abx + -1c + -7x = -3b Add 'c' to each side of the equation. 8a + abx + -1c + c + -7x = -3b + c Combine like terms: -1c + c = 0 8a + abx + 0 + -7x = -3b + c 8a + abx + -7x = -3b + c Add '7x' to each side of the equation. 8a + abx + -7x + 7x = -3b + c + 7x Combine like terms: -7x + 7x = 0 8a + abx + 0 = -3b + c + 7x 8a + abx = -3b + c + 7x 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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