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Simplifying (3x + 2)(3x + 2) = 4(2x + -3)(2x + -3) Reorder the terms: (2 + 3x)(3x + 2) = 4(2x + -3)(2x + -3) Reorder the terms: (2 + 3x)(2 + 3x) = 4(2x + -3)(2x + -3) Multiply (2 + 3x) * (2 + 3x) (2(2 + 3x) + 3x * (2 + 3x)) = 4(2x + -3)(2x + -3) ((2 * 2 + 3x * 2) + 3x * (2 + 3x)) = 4(2x + -3)(2x + -3) ((4 + 6x) + 3x * (2 + 3x)) = 4(2x + -3)(2x + -3) (4 + 6x + (2 * 3x + 3x * 3x)) = 4(2x + -3)(2x + -3) (4 + 6x + (6x + 9x2)) = 4(2x + -3)(2x + -3) Combine like terms: 6x + 6x = 12x (4 + 12x + 9x2) = 4(2x + -3)(2x + -3) Reorder the terms: 4 + 12x + 9x2 = 4(-3 + 2x)(2x + -3) Reorder the terms: 4 + 12x + 9x2 = 4(-3 + 2x)(-3 + 2x) Multiply (-3 + 2x) * (-3 + 2x) 4 + 12x + 9x2 = 4(-3(-3 + 2x) + 2x * (-3 + 2x)) 4 + 12x + 9x2 = 4((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) 4 + 12x + 9x2 = 4((9 + -6x) + 2x * (-3 + 2x)) 4 + 12x + 9x2 = 4(9 + -6x + (-3 * 2x + 2x * 2x)) 4 + 12x + 9x2 = 4(9 + -6x + (-6x + 4x2)) Combine like terms: -6x + -6x = -12x 4 + 12x + 9x2 = 4(9 + -12x + 4x2) 4 + 12x + 9x2 = (9 * 4 + -12x * 4 + 4x2 * 4) 4 + 12x + 9x2 = (36 + -48x + 16x2) Solving 4 + 12x + 9x2 = 36 + -48x + 16x2 Solving for variable 'x'. Reorder the terms: 4 + -36 + 12x + 48x + 9x2 + -16x2 = 36 + -48x + 16x2 + -36 + 48x + -16x2 Combine like terms: 4 + -36 = -32 -32 + 12x + 48x + 9x2 + -16x2 = 36 + -48x + 16x2 + -36 + 48x + -16x2 Combine like terms: 12x + 48x = 60x -32 + 60x + 9x2 + -16x2 = 36 + -48x + 16x2 + -36 + 48x + -16x2 Combine like terms: 9x2 + -16x2 = -7x2 -32 + 60x + -7x2 = 36 + -48x + 16x2 + -36 + 48x + -16x2 Reorder the terms: -32 + 60x + -7x2 = 36 + -36 + -48x + 48x + 16x2 + -16x2 Combine like terms: 36 + -36 = 0 -32 + 60x + -7x2 = 0 + -48x + 48x + 16x2 + -16x2 -32 + 60x + -7x2 = -48x + 48x + 16x2 + -16x2 Combine like terms: -48x + 48x = 0 -32 + 60x + -7x2 = 0 + 16x2 + -16x2 -32 + 60x + -7x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -32 + 60x + -7x2 = 0 Factor a trinomial. (-8 + x)(4 + -7x) = 0Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714Solution
x = {8, 0.5714285714}
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