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Simplifying (3X + 2)(3X + -4) = -3(4X + 3) Reorder the terms: (2 + 3X)(3X + -4) = -3(4X + 3) Reorder the terms: (2 + 3X)(-4 + 3X) = -3(4X + 3) Multiply (2 + 3X) * (-4 + 3X) (2(-4 + 3X) + 3X * (-4 + 3X)) = -3(4X + 3) ((-4 * 2 + 3X * 2) + 3X * (-4 + 3X)) = -3(4X + 3) ((-8 + 6X) + 3X * (-4 + 3X)) = -3(4X + 3) (-8 + 6X + (-4 * 3X + 3X * 3X)) = -3(4X + 3) (-8 + 6X + (-12X + 9X2)) = -3(4X + 3) Combine like terms: 6X + -12X = -6X (-8 + -6X + 9X2) = -3(4X + 3) Reorder the terms: -8 + -6X + 9X2 = -3(3 + 4X) -8 + -6X + 9X2 = (3 * -3 + 4X * -3) -8 + -6X + 9X2 = (-9 + -12X) Solving -8 + -6X + 9X2 = -9 + -12X Solving for variable 'X'. Reorder the terms: -8 + 9 + -6X + 12X + 9X2 = -9 + -12X + 9 + 12X Combine like terms: -8 + 9 = 1 1 + -6X + 12X + 9X2 = -9 + -12X + 9 + 12X Combine like terms: -6X + 12X = 6X 1 + 6X + 9X2 = -9 + -12X + 9 + 12X Reorder the terms: 1 + 6X + 9X2 = -9 + 9 + -12X + 12X Combine like terms: -9 + 9 = 0 1 + 6X + 9X2 = 0 + -12X + 12X 1 + 6X + 9X2 = -12X + 12X Combine like terms: -12X + 12X = 0 1 + 6X + 9X2 = 0 Factor a trinomial. (1 + 3X)(1 + 3X) = 0Subproblem 1
Set the factor '(1 + 3X)' equal to zero and attempt to solve: Simplifying 1 + 3X = 0 Solving 1 + 3X = 0 Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3X = 0 + -1 3X = 0 + -1 Combine like terms: 0 + -1 = -1 3X = -1 Divide each side by '3'. X = -0.3333333333 Simplifying X = -0.3333333333Subproblem 2
Set the factor '(1 + 3X)' equal to zero and attempt to solve: Simplifying 1 + 3X = 0 Solving 1 + 3X = 0 Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3X = 0 + -1 3X = 0 + -1 Combine like terms: 0 + -1 = -1 3X = -1 Divide each side by '3'. X = -0.3333333333 Simplifying X = -0.3333333333Solution
X = {-0.3333333333, -0.3333333333}
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