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Simplifying r^{2}+ -12r + 35 = 0 Reorder the terms: 35 + -12r + r^{2}= 0 Solving 35 + -12r + r^{2}= 0 Solving for variable 'r'. Factor a trinomial. (5 + -1r)(7 + -1r) = 0## Subproblem 1

Set the factor '(5 + -1r)' equal to zero and attempt to solve: Simplifying 5 + -1r = 0 Solving 5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1r = 0 + -5 -1r = 0 + -5 Combine like terms: 0 + -5 = -5 -1r = -5 Divide each side by '-1'. r = 5 Simplifying r = 5## Subproblem 2

Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7## Solution

r = {5, 7}

| m^2-5m=0 | | 5x^2=50 | | t^2+7t-35=2t-11 | | 2(x^2)-7x=1 | | x^2+4x-2m=0 | | 27x^2-5x=0 | | 7e^8+t=2 | | 13x^2-28x=0 | | 15n+3n^4-4n+12n^4+n= | | 2x^2-24x=-2x^2-7x-18 | | 30x^3-9x^2-3x=0 | | x^2+4=17 | | (x^3+2x+3x+6)= | | (2x^3+3)= | | (x^2+3)(x^3+2x^2+3x+6)+(2x^3+3)= | | 10y^2+33y+20=0 | | y^3+8y^2+16y=0 | | x^2+4x-60=0 | | 14x^2-5x=0 | | (x^3+y^5)(x^3-y^5)= | | 5x^2+11x+1=0 | | y^2-16y-4= | | y=5x^2-3x+5 | | 7x-28=2x^2-8x-3x+12 | | y=x^2+5x | | y=x^2+2x | | x^7-5x^5+x^2-5=0 | | 15x^2-8x-7=0 | | X^2+6x-27=0 | | 3x^2-6x+12=0 | | (4x^3-6x^2+5)-(8x^2+3x-6)= | | 11x^2-2x+9=0 |

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