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Simplifying lg(3x + -6) * lg(2x + -3) = 0 Reorder the terms: gl(-6 + 3x) * lg(2x + -3) = 0 Reorder the terms: gl(-6 + 3x) * gl(-3 + 2x) = 0 Reorder the terms for easier multiplication: gl * gl(-6 + 3x)(-3 + 2x) = 0 Multiply gl * gl g2l2(-6 + 3x)(-3 + 2x) = 0 Multiply (-6 + 3x) * (-3 + 2x) g2l2(-6(-3 + 2x) + 3x * (-3 + 2x)) = 0 g2l2((-3 * -6 + 2x * -6) + 3x * (-3 + 2x)) = 0 g2l2((18 + -12x) + 3x * (-3 + 2x)) = 0 g2l2(18 + -12x + (-3 * 3x + 2x * 3x)) = 0 g2l2(18 + -12x + (-9x + 6x2)) = 0 Combine like terms: -12x + -9x = -21x g2l2(18 + -21x + 6x2) = 0 (18 * g2l2 + -21x * g2l2 + 6x2 * g2l2) = 0 (18g2l2 + -21g2l2x + 6g2l2x2) = 0 Solving 18g2l2 + -21g2l2x + 6g2l2x2 = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3g2l2'. 3g2l2(6 + -7x + 2x2) = 0 Factor a trinomial. 3g2l2((3 + -2x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'g2l2' equal to zero and attempt to solve: Simplifying g2l2 = 0 Solving g2l2 = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g2l2 = 0 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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