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Simplifying (4x + -7)(2x + 3) = 3(4x + -7)(5x + 11) Reorder the terms: (-7 + 4x)(2x + 3) = 3(4x + -7)(5x + 11) Reorder the terms: (-7 + 4x)(3 + 2x) = 3(4x + -7)(5x + 11) Multiply (-7 + 4x) * (3 + 2x) (-7(3 + 2x) + 4x * (3 + 2x)) = 3(4x + -7)(5x + 11) ((3 * -7 + 2x * -7) + 4x * (3 + 2x)) = 3(4x + -7)(5x + 11) ((-21 + -14x) + 4x * (3 + 2x)) = 3(4x + -7)(5x + 11) (-21 + -14x + (3 * 4x + 2x * 4x)) = 3(4x + -7)(5x + 11) (-21 + -14x + (12x + 8x2)) = 3(4x + -7)(5x + 11) Combine like terms: -14x + 12x = -2x (-21 + -2x + 8x2) = 3(4x + -7)(5x + 11) Reorder the terms: -21 + -2x + 8x2 = 3(-7 + 4x)(5x + 11) Reorder the terms: -21 + -2x + 8x2 = 3(-7 + 4x)(11 + 5x) Multiply (-7 + 4x) * (11 + 5x) -21 + -2x + 8x2 = 3(-7(11 + 5x) + 4x * (11 + 5x)) -21 + -2x + 8x2 = 3((11 * -7 + 5x * -7) + 4x * (11 + 5x)) -21 + -2x + 8x2 = 3((-77 + -35x) + 4x * (11 + 5x)) -21 + -2x + 8x2 = 3(-77 + -35x + (11 * 4x + 5x * 4x)) -21 + -2x + 8x2 = 3(-77 + -35x + (44x + 20x2)) Combine like terms: -35x + 44x = 9x -21 + -2x + 8x2 = 3(-77 + 9x + 20x2) -21 + -2x + 8x2 = (-77 * 3 + 9x * 3 + 20x2 * 3) -21 + -2x + 8x2 = (-231 + 27x + 60x2) Solving -21 + -2x + 8x2 = -231 + 27x + 60x2 Solving for variable 'x'. Reorder the terms: -21 + 231 + -2x + -27x + 8x2 + -60x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2 Combine like terms: -21 + 231 = 210 210 + -2x + -27x + 8x2 + -60x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2 Combine like terms: -2x + -27x = -29x 210 + -29x + 8x2 + -60x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2 Combine like terms: 8x2 + -60x2 = -52x2 210 + -29x + -52x2 = -231 + 27x + 60x2 + 231 + -27x + -60x2 Reorder the terms: 210 + -29x + -52x2 = -231 + 231 + 27x + -27x + 60x2 + -60x2 Combine like terms: -231 + 231 = 0 210 + -29x + -52x2 = 0 + 27x + -27x + 60x2 + -60x2 210 + -29x + -52x2 = 27x + -27x + 60x2 + -60x2 Combine like terms: 27x + -27x = 0 210 + -29x + -52x2 = 0 + 60x2 + -60x2 210 + -29x + -52x2 = 60x2 + -60x2 Combine like terms: 60x2 + -60x2 = 0 210 + -29x + -52x2 = 0 Factor a trinomial. (7 + -4x)(30 + 13x) = 0Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Subproblem 2
Set the factor '(30 + 13x)' equal to zero and attempt to solve: Simplifying 30 + 13x = 0 Solving 30 + 13x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + 13x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 13x = 0 + -30 13x = 0 + -30 Combine like terms: 0 + -30 = -30 13x = -30 Divide each side by '13'. x = -2.307692308 Simplifying x = -2.307692308Solution
x = {1.75, -2.307692308}
| -3(x+2)-5x=-9 | | 32=24x+23 | | 25(x-2)=5(5x-10) | | 3x^2+27+60=0 | | 2lnx=ln(2x+3) | | 60x^4+59x^3-45x^2-14x=0 | | 2(4.2x-3)=4(2.1x+1) | | .7(x+90)+.9x=127 | | 7b(a-4)-3(a-4)= | | -22=- (x-4) | | 1.75b=7.75b-12 | | -(6y+3)-(-5y-7)=3 | | 8-(-11)= | | 0.8x-15=0.4-0.2x | | 6x(8x+1)+1(8x+1)= | | -33.66x+19.2=4.75 | | 2a^2+9=0 | | 5[-2p+20]=25 | | -15-2= | | 3(2x-3)-5=16 | | 3(23-x)=15-(x-6) | | 16t^2+64t+40=0 | | -5*3= | | 6.5(m-5)=2(0.75-m) | | 3x^2+11x+3=0 | | b^2+49= | | .2(x)+18=75 | | 9x+2+4x+9=12x+3 | | 3(h+2)+h=15-(h+4) | | 3p+8=2p+17 | | .3(x)-36=6 | | 6(x+3)-10=32 |