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Simplifying 18x2 + -3x + -36 = 3(3x + a)(2x + -1b) Reorder the terms: -36 + -3x + 18x2 = 3(3x + a)(2x + -1b) Reorder the terms: -36 + -3x + 18x2 = 3(a + 3x)(2x + -1b) Reorder the terms: -36 + -3x + 18x2 = 3(a + 3x)(-1b + 2x) Multiply (a + 3x) * (-1b + 2x) -36 + -3x + 18x2 = 3(a(-1b + 2x) + 3x * (-1b + 2x)) -36 + -3x + 18x2 = 3((-1b * a + 2x * a) + 3x * (-1b + 2x)) -36 + -3x + 18x2 = 3((-1ab + 2ax) + 3x * (-1b + 2x)) -36 + -3x + 18x2 = 3(-1ab + 2ax + (-1b * 3x + 2x * 3x)) -36 + -3x + 18x2 = 3(-1ab + 2ax + (-3bx + 6x2)) -36 + -3x + 18x2 = 3(-1ab + 2ax + -3bx + 6x2) -36 + -3x + 18x2 = (-1ab * 3 + 2ax * 3 + -3bx * 3 + 6x2 * 3) -36 + -3x + 18x2 = (-3ab + 6ax + -9bx + 18x2) Add '-18x2' to each side of the equation. -36 + -3x + 18x2 + -18x2 = -3ab + 6ax + -9bx + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -36 + -3x + 0 = -3ab + 6ax + -9bx + 18x2 + -18x2 -36 + -3x = -3ab + 6ax + -9bx + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -36 + -3x = -3ab + 6ax + -9bx + 0 -36 + -3x = -3ab + 6ax + -9bx Solving -36 + -3x = -3ab + 6ax + -9bx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6ax' to each side of the equation. -36 + -6ax + -3x = -3ab + 6ax + -6ax + -9bx Combine like terms: 6ax + -6ax = 0 -36 + -6ax + -3x = -3ab + 0 + -9bx -36 + -6ax + -3x = -3ab + -9bx Add '9bx' to each side of the equation. -36 + -6ax + 9bx + -3x = -3ab + -9bx + 9bx Combine like terms: -9bx + 9bx = 0 -36 + -6ax + 9bx + -3x = -3ab + 0 -36 + -6ax + 9bx + -3x = -3ab Add '36' to each side of the equation. -36 + -6ax + 9bx + 36 + -3x = 36 + -3ab Reorder the terms: -36 + 36 + -6ax + 9bx + -3x = 36 + -3ab Combine like terms: -36 + 36 = 0 0 + -6ax + 9bx + -3x = 36 + -3ab -6ax + 9bx + -3x = 36 + -3ab Reorder the terms: -36 + 3ab + -6ax + 9bx + -3x = 36 + -3ab + -36 + 3ab Reorder the terms: -36 + 3ab + -6ax + 9bx + -3x = 36 + -36 + -3ab + 3ab Combine like terms: 36 + -36 = 0 -36 + 3ab + -6ax + 9bx + -3x = 0 + -3ab + 3ab -36 + 3ab + -6ax + 9bx + -3x = -3ab + 3ab Combine like terms: -3ab + 3ab = 0 -36 + 3ab + -6ax + 9bx + -3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + ab + -2ax + 3bx + -1x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + ab + -2ax + 3bx + -1x)' equal to zero and attempt to solve: Simplifying -12 + ab + -2ax + 3bx + -1x = 0 Solving -12 + ab + -2ax + 3bx + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + ab + -2ax + 3bx + 12 + -1x = 0 + 12 Reorder the terms: -12 + 12 + ab + -2ax + 3bx + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + ab + -2ax + 3bx + -1x = 0 + 12 ab + -2ax + 3bx + -1x = 0 + 12 Combine like terms: 0 + 12 = 12 ab + -2ax + 3bx + -1x = 12 Add '-1ab' to each side of the equation. ab + -2ax + 3bx + -1ab + -1x = 12 + -1ab Reorder the terms: ab + -1ab + -2ax + 3bx + -1x = 12 + -1ab Combine like terms: ab + -1ab = 0 0 + -2ax + 3bx + -1x = 12 + -1ab -2ax + 3bx + -1x = 12 + -1ab 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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