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Simplifying -1x = 2x^{2}+ -6 Reorder the terms: -1x = -6 + 2x^{2}Solving -1x = -6 + 2x^{2}Solving for variable 'x'. Reorder the terms: 6 + -1x + -2x^{2}= -6 + 2x^{2}+ 6 + -2x^{2}Reorder the terms: 6 + -1x + -2x^{2}= -6 + 6 + 2x^{2}+ -2x^{2}Combine like terms: -6 + 6 = 0 6 + -1x + -2x^{2}= 0 + 2x^{2}+ -2x^{2}6 + -1x + -2x^{2}= 2x^{2}+ -2x^{2}Combine like terms: 2x^{2}+ -2x^{2}= 0 6 + -1x + -2x^{2}= 0 Factor a trinomial. (3 + -2x)(2 + x) = 0## Subproblem 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 = 1.5## Subproblem 2

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 = -2## Solution

x = {1.5, -2}

| -2x=3x^2-1 | | -9x=2x^2-5 | | x^2-5x-6=0 | | x^2-x-12=0 | | 3x^2+5x-13=11-9x | | 5x^3-5x=0 | | 16x^2+2x-3=0 | | 4x^2-25=0 | | x^2-19x=0 | | x^2-x+18=0 | | 13x^2-11x=0 | | 7x^2+4x-15=49-44x | | 3x^3+9x^2+6x=0 | | x^2-3x-18=0 | | x^2-63x+60=0 | | 2x(4x-7)+3=(2x-7)(3x+4)+2x^2 | | 8x^3+10xy+6x^2y^5=0 | | 2X(X^2-4X+7)= | | 2x^2-5x-5=0 | | 2x^2-38x=7x^2-3x-24 | | 9p^2+18p=10 | | x^2-5x=6 | | 2x^2-4=-204 | | 2x^2-8=-170 | | x(5x+10)=2x^2-3x+30 | | 8x^2-8x-1=0 | | 2x^2-9x-2=0 | | 2x^2=10x+3 | | y^2-4y+8=0 | | 42t^2-13tv-42v^2= | | 6s^2-13s+6= | | 2w^2+9w+9= |

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