To find the solution to the given equations, we will simplify each equation separately.
1) 12x(x-3) = (6-x)(x+2Expanding the left side12x^2 - 36x
Expanding the right side6x^2 + 12x - x^2 - 26x^2 + 12x - x^2 - 25x^2 + 10x
Now, equating the left and right sides12x^2 - 36x = 5x^2 + 10x
Rearranging the terms12x^2 - 5x^2 - 36x - 10x = 7x^2 - 46x = x(7x - 46) = 0
Setting each factor to zerox = 0 or 7x - 46 = x = 0 or x = 46/7
Therefore, the solutions to the first equation are x = 0 and x = (46/7).
2) (1-2x)(1-3x) = (6x-1)x - Expanding the left side1 - 3x - 2x + 6x^1 - 5x + 6x^2
Expanding the right side6x^2 - x - 6x^2 - x - 1
Now, equating the left and right sides1 - 5x + 6x^2 = 6x^2 - x - 1 - 5x + 6x^2 = 6x^2 - x - 1
Subtracting the common terms-5x = -x - -5x + x = --4x = -x = -2/-x = 1/2
Therefore, the solution to the second equation is x = 1/2.
In conclusion, the solutions to the given equations arex = 0, x = 46/7, and x = 1/2.
To find the solution to the given equations, we will simplify each equation separately.
1) 12x(x-3) = (6-x)(x+2
Expanding the left side
12x^2 - 36x
Expanding the right side
6x^2 + 12x - x^2 - 2
6x^2 + 12x - x^2 - 2
5x^2 + 10x
Now, equating the left and right sides
12x^2 - 36x = 5x^2 + 10x
Rearranging the terms
12x^2 - 5x^2 - 36x - 10x =
7x^2 - 46x =
x(7x - 46) = 0
Setting each factor to zero
x = 0 or 7x - 46 =
x = 0 or x = 46/7
Therefore, the solutions to the first equation are x = 0 and x = (46/7).
2) (1-2x)(1-3x) = (6x-1)x -
Expanding the left side
1 - 3x - 2x + 6x^
1 - 5x + 6x^2
Expanding the right side
6x^2 - x -
6x^2 - x - 1
Now, equating the left and right sides
1 - 5x + 6x^2 = 6x^2 - x -
1 - 5x + 6x^2 = 6x^2 - x - 1
Subtracting the common terms
-5x = -x -
-5x + x = -
-4x = -
x = -2/-
x = 1/2
Therefore, the solution to the second equation is x = 1/2.
In conclusion, the solutions to the given equations are
x = 0, x = 46/7, and x = 1/2.