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Simplifying (4b + 2)(3b + -9a) = 0 Reorder the terms: (2 + 4b)(3b + -9a) = 0 Reorder the terms: (2 + 4b)(-9a + 3b) = 0 Multiply (2 + 4b) * (-9a + 3b) (2(-9a + 3b) + 4b * (-9a + 3b)) = 0 ((-9a * 2 + 3b * 2) + 4b * (-9a + 3b)) = 0 ((-18a + 6b) + 4b * (-9a + 3b)) = 0 (-18a + 6b + (-9a * 4b + 3b * 4b)) = 0 (-18a + 6b + (-36ab + 12b2)) = 0 Reorder the terms: (-18a + -36ab + 6b + 12b2) = 0 (-18a + -36ab + 6b + 12b2) = 0 Solving -18a + -36ab + 6b + 12b2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. -18a + -36ab + 6b + -6b + 12b2 = 0 + -6b Combine like terms: 6b + -6b = 0 -18a + -36ab + 0 + 12b2 = 0 + -6b -18a + -36ab + 12b2 = 0 + -6b Remove the zero: -18a + -36ab + 12b2 = -6b Add '-12b2' to each side of the equation. -18a + -36ab + 12b2 + -12b2 = -6b + -12b2 Combine like terms: 12b2 + -12b2 = 0 -18a + -36ab + 0 = -6b + -12b2 -18a + -36ab = -6b + -12b2 Reorder the terms: -18a + -36ab + 6b + 12b2 = -6b + 6b + -12b2 + 12b2 Combine like terms: -6b + 6b = 0 -18a + -36ab + 6b + 12b2 = 0 + -12b2 + 12b2 -18a + -36ab + 6b + 12b2 = -12b2 + 12b2 Combine like terms: -12b2 + 12b2 = 0 -18a + -36ab + 6b + 12b2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3a + -6ab + b + 2b2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3a + -6ab + b + 2b2)' equal to zero and attempt to solve: Simplifying -3a + -6ab + b + 2b2 = 0 Solving -3a + -6ab + b + 2b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -3a + -6ab + b + -1b + 2b2 = 0 + -1b Combine like terms: b + -1b = 0 -3a + -6ab + 0 + 2b2 = 0 + -1b -3a + -6ab + 2b2 = 0 + -1b Remove the zero: -3a + -6ab + 2b2 = -1b Add '-2b2' to each side of the equation. -3a + -6ab + 2b2 + -2b2 = -1b + -2b2 Combine like terms: 2b2 + -2b2 = 0 -3a + -6ab + 0 = -1b + -2b2 -3a + -6ab = -1b + -2b2 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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