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Simplifying (3x + -2)(3x + 2) + -1(2x + -5)(8x + -3) = 4x + -19 Reorder the terms: (-2 + 3x)(3x + 2) + -1(2x + -5)(8x + -3) = 4x + -19 Reorder the terms: (-2 + 3x)(2 + 3x) + -1(2x + -5)(8x + -3) = 4x + -19 Multiply (-2 + 3x) * (2 + 3x) (-2(2 + 3x) + 3x * (2 + 3x)) + -1(2x + -5)(8x + -3) = 4x + -19 ((2 * -2 + 3x * -2) + 3x * (2 + 3x)) + -1(2x + -5)(8x + -3) = 4x + -19 ((-4 + -6x) + 3x * (2 + 3x)) + -1(2x + -5)(8x + -3) = 4x + -19 (-4 + -6x + (2 * 3x + 3x * 3x)) + -1(2x + -5)(8x + -3) = 4x + -19 (-4 + -6x + (6x + 9x2)) + -1(2x + -5)(8x + -3) = 4x + -19 Combine like terms: -6x + 6x = 0 (-4 + 0 + 9x2) + -1(2x + -5)(8x + -3) = 4x + -19 (-4 + 9x2) + -1(2x + -5)(8x + -3) = 4x + -19 Reorder the terms: -4 + 9x2 + -1(-5 + 2x)(8x + -3) = 4x + -19 Reorder the terms: -4 + 9x2 + -1(-5 + 2x)(-3 + 8x) = 4x + -19 Multiply (-5 + 2x) * (-3 + 8x) -4 + 9x2 + -1(-5(-3 + 8x) + 2x * (-3 + 8x)) = 4x + -19 -4 + 9x2 + -1((-3 * -5 + 8x * -5) + 2x * (-3 + 8x)) = 4x + -19 -4 + 9x2 + -1((15 + -40x) + 2x * (-3 + 8x)) = 4x + -19 -4 + 9x2 + -1(15 + -40x + (-3 * 2x + 8x * 2x)) = 4x + -19 -4 + 9x2 + -1(15 + -40x + (-6x + 16x2)) = 4x + -19 Combine like terms: -40x + -6x = -46x -4 + 9x2 + -1(15 + -46x + 16x2) = 4x + -19 -4 + 9x2 + (15 * -1 + -46x * -1 + 16x2 * -1) = 4x + -19 -4 + 9x2 + (-15 + 46x + -16x2) = 4x + -19 Reorder the terms: -4 + -15 + 46x + 9x2 + -16x2 = 4x + -19 Combine like terms: -4 + -15 = -19 -19 + 46x + 9x2 + -16x2 = 4x + -19 Combine like terms: 9x2 + -16x2 = -7x2 -19 + 46x + -7x2 = 4x + -19 Reorder the terms: -19 + 46x + -7x2 = -19 + 4x Add '19' to each side of the equation. -19 + 46x + 19 + -7x2 = -19 + 19 + 4x Reorder the terms: -19 + 19 + 46x + -7x2 = -19 + 19 + 4x Combine like terms: -19 + 19 = 0 0 + 46x + -7x2 = -19 + 19 + 4x 46x + -7x2 = -19 + 19 + 4x Combine like terms: -19 + 19 = 0 46x + -7x2 = 0 + 4x 46x + -7x2 = 4x Solving 46x + -7x2 = 4x Solving for variable 'x'. Reorder the terms: 46x + -4x + -7x2 = 4x + -4x Combine like terms: 46x + -4x = 42x 42x + -7x2 = 4x + -4x Combine like terms: 4x + -4x = 0 42x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '7x'. 7x(6 + -1x) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 6}
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