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Simplifying (-2x + 3)(x + -3) + (-2x + 3)(2x + 5) = 0 Reorder the terms: (3 + -2x)(x + -3) + (-2x + 3)(2x + 5) = 0 Reorder the terms: (3 + -2x)(-3 + x) + (-2x + 3)(2x + 5) = 0 Multiply (3 + -2x) * (-3 + x) (3(-3 + x) + -2x * (-3 + x)) + (-2x + 3)(2x + 5) = 0 ((-3 * 3 + x * 3) + -2x * (-3 + x)) + (-2x + 3)(2x + 5) = 0 ((-9 + 3x) + -2x * (-3 + x)) + (-2x + 3)(2x + 5) = 0 (-9 + 3x + (-3 * -2x + x * -2x)) + (-2x + 3)(2x + 5) = 0 (-9 + 3x + (6x + -2x2)) + (-2x + 3)(2x + 5) = 0 Combine like terms: 3x + 6x = 9x (-9 + 9x + -2x2) + (-2x + 3)(2x + 5) = 0 Reorder the terms: -9 + 9x + -2x2 + (3 + -2x)(2x + 5) = 0 Reorder the terms: -9 + 9x + -2x2 + (3 + -2x)(5 + 2x) = 0 Multiply (3 + -2x) * (5 + 2x) -9 + 9x + -2x2 + (3(5 + 2x) + -2x * (5 + 2x)) = 0 -9 + 9x + -2x2 + ((5 * 3 + 2x * 3) + -2x * (5 + 2x)) = 0 -9 + 9x + -2x2 + ((15 + 6x) + -2x * (5 + 2x)) = 0 -9 + 9x + -2x2 + (15 + 6x + (5 * -2x + 2x * -2x)) = 0 -9 + 9x + -2x2 + (15 + 6x + (-10x + -4x2)) = 0 Combine like terms: 6x + -10x = -4x -9 + 9x + -2x2 + (15 + -4x + -4x2) = 0 Reorder the terms: -9 + 15 + 9x + -4x + -2x2 + -4x2 = 0 Combine like terms: -9 + 15 = 6 6 + 9x + -4x + -2x2 + -4x2 = 0 Combine like terms: 9x + -4x = 5x 6 + 5x + -2x2 + -4x2 = 0 Combine like terms: -2x2 + -4x2 = -6x2 6 + 5x + -6x2 = 0 Solving 6 + 5x + -6x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + -2x)(2 + 3x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x 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 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {1.5, -0.6666666667}
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