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Simplifying (9 + -5x)(3x + -4) + 30 = 2(3x + -4)(6x + -5) Reorder the terms: (9 + -5x)(-4 + 3x) + 30 = 2(3x + -4)(6x + -5) Multiply (9 + -5x) * (-4 + 3x) (9(-4 + 3x) + -5x * (-4 + 3x)) + 30 = 2(3x + -4)(6x + -5) ((-4 * 9 + 3x * 9) + -5x * (-4 + 3x)) + 30 = 2(3x + -4)(6x + -5) ((-36 + 27x) + -5x * (-4 + 3x)) + 30 = 2(3x + -4)(6x + -5) (-36 + 27x + (-4 * -5x + 3x * -5x)) + 30 = 2(3x + -4)(6x + -5) (-36 + 27x + (20x + -15x2)) + 30 = 2(3x + -4)(6x + -5) Combine like terms: 27x + 20x = 47x (-36 + 47x + -15x2) + 30 = 2(3x + -4)(6x + -5) Reorder the terms: -36 + 30 + 47x + -15x2 = 2(3x + -4)(6x + -5) Combine like terms: -36 + 30 = -6 -6 + 47x + -15x2 = 2(3x + -4)(6x + -5) Reorder the terms: -6 + 47x + -15x2 = 2(-4 + 3x)(6x + -5) Reorder the terms: -6 + 47x + -15x2 = 2(-4 + 3x)(-5 + 6x) Multiply (-4 + 3x) * (-5 + 6x) -6 + 47x + -15x2 = 2(-4(-5 + 6x) + 3x * (-5 + 6x)) -6 + 47x + -15x2 = 2((-5 * -4 + 6x * -4) + 3x * (-5 + 6x)) -6 + 47x + -15x2 = 2((20 + -24x) + 3x * (-5 + 6x)) -6 + 47x + -15x2 = 2(20 + -24x + (-5 * 3x + 6x * 3x)) -6 + 47x + -15x2 = 2(20 + -24x + (-15x + 18x2)) Combine like terms: -24x + -15x = -39x -6 + 47x + -15x2 = 2(20 + -39x + 18x2) -6 + 47x + -15x2 = (20 * 2 + -39x * 2 + 18x2 * 2) -6 + 47x + -15x2 = (40 + -78x + 36x2) Solving -6 + 47x + -15x2 = 40 + -78x + 36x2 Solving for variable 'x'. Reorder the terms: -6 + -40 + 47x + 78x + -15x2 + -36x2 = 40 + -78x + 36x2 + -40 + 78x + -36x2 Combine like terms: -6 + -40 = -46 -46 + 47x + 78x + -15x2 + -36x2 = 40 + -78x + 36x2 + -40 + 78x + -36x2 Combine like terms: 47x + 78x = 125x -46 + 125x + -15x2 + -36x2 = 40 + -78x + 36x2 + -40 + 78x + -36x2 Combine like terms: -15x2 + -36x2 = -51x2 -46 + 125x + -51x2 = 40 + -78x + 36x2 + -40 + 78x + -36x2 Reorder the terms: -46 + 125x + -51x2 = 40 + -40 + -78x + 78x + 36x2 + -36x2 Combine like terms: 40 + -40 = 0 -46 + 125x + -51x2 = 0 + -78x + 78x + 36x2 + -36x2 -46 + 125x + -51x2 = -78x + 78x + 36x2 + -36x2 Combine like terms: -78x + 78x = 0 -46 + 125x + -51x2 = 0 + 36x2 + -36x2 -46 + 125x + -51x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 -46 + 125x + -51x2 = 0 Factor a trinomial. (-2 + x)(23 + -51x) = 0Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(23 + -51x)' equal to zero and attempt to solve: Simplifying 23 + -51x = 0 Solving 23 + -51x = 0 Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + -51x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -51x = 0 + -23 -51x = 0 + -23 Combine like terms: 0 + -23 = -23 -51x = -23 Divide each side by '-51'. x = 0.4509803922 Simplifying x = 0.4509803922Solution
x = {2, 0.4509803922}
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