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Simplifying (ax + 4)(x + -2) = 3x2 + bx + -8 Reorder the terms: (4 + ax)(x + -2) = 3x2 + bx + -8 Reorder the terms: (4 + ax)(-2 + x) = 3x2 + bx + -8 Multiply (4 + ax) * (-2 + x) (4(-2 + x) + ax(-2 + x)) = 3x2 + bx + -8 ((-2 * 4 + x * 4) + ax(-2 + x)) = 3x2 + bx + -8 ((-8 + 4x) + ax(-2 + x)) = 3x2 + bx + -8 (-8 + 4x + (-2 * ax + x * ax)) = 3x2 + bx + -8 (-8 + 4x + (-2ax + ax2)) = 3x2 + bx + -8 Reorder the terms: (-8 + -2ax + ax2 + 4x) = 3x2 + bx + -8 (-8 + -2ax + ax2 + 4x) = 3x2 + bx + -8 Reorder the terms: -8 + -2ax + ax2 + 4x = -8 + bx + 3x2 Add '8' to each side of the equation. -8 + -2ax + ax2 + 8 + 4x = -8 + bx + 8 + 3x2 Reorder the terms: -8 + 8 + -2ax + ax2 + 4x = -8 + bx + 8 + 3x2 Combine like terms: -8 + 8 = 0 0 + -2ax + ax2 + 4x = -8 + bx + 8 + 3x2 -2ax + ax2 + 4x = -8 + bx + 8 + 3x2 Reorder the terms: -2ax + ax2 + 4x = -8 + 8 + bx + 3x2 Combine like terms: -8 + 8 = 0 -2ax + ax2 + 4x = 0 + bx + 3x2 -2ax + ax2 + 4x = bx + 3x2 Solving -2ax + ax2 + 4x = bx + 3x2 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4x' to each side of the equation. -2ax + ax2 + 4x + -4x = bx + -4x + 3x2 Combine like terms: 4x + -4x = 0 -2ax + ax2 + 0 = bx + -4x + 3x2 -2ax + ax2 = bx + -4x + 3x2 Reorder the terms: -2ax + ax2 + -1bx + 4x + -3x2 = bx + -1bx + -4x + 4x + 3x2 + -3x2 Combine like terms: bx + -1bx = 0 -2ax + ax2 + -1bx + 4x + -3x2 = 0 + -4x + 4x + 3x2 + -3x2 -2ax + ax2 + -1bx + 4x + -3x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 -2ax + ax2 + -1bx + 4x + -3x2 = 0 + 3x2 + -3x2 -2ax + ax2 + -1bx + 4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -2ax + ax2 + -1bx + 4x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2a + ax + -1b + 4 + -3x) = 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 '(-2a + ax + -1b + 4 + -3x)' equal to zero and attempt to solve: Simplifying -2a + ax + -1b + 4 + -3x = 0 Reorder the terms: 4 + -2a + ax + -1b + -3x = 0 Solving 4 + -2a + ax + -1b + -3x = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -2a + ax + -1b + -4 + -3x = 0 + -4 Reorder the terms: 4 + -4 + -2a + ax + -1b + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2a + ax + -1b + -3x = 0 + -4 -2a + ax + -1b + -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -2a + ax + -1b + -3x = -4 Add 'b' to each side of the equation. -2a + ax + -1b + b + -3x = -4 + b Combine like terms: -1b + b = 0 -2a + ax + 0 + -3x = -4 + b -2a + ax + -3x = -4 + b Add '3x' to each side of the equation. -2a + ax + -3x + 3x = -4 + b + 3x Combine like terms: -3x + 3x = 0 -2a + ax + 0 = -4 + b + 3x -2a + ax = -4 + b + 3x 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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