The general form of quadratic equation with one variable - 2x ^ 2-12x = 3 (1-x) (x-1)

The general form of quadratic equation with one variable - 2x ^ 2-12x = 3 (1-x) (x-1)

-2x²-12x=-3(x²-2x+1)
x²-18x+3=0

(2x-2) (x-1) = 0 into the general form of quadratic equation with one variable?

How can 1 / 2x ^ 2-x = 2 be transformed into the general form of - 1 / 2x ^ 2 + X + 2 = 0 univariate quadratic equation?

1 / 2x ^ 2-x = 2 move 2 to the left
1 / 2x ^ 2-x-2 = 0 multiply by - 1
-1/2x^2+x+2=0

(2x-2) (x-1) = 0 is transformed into a form of quadratic equation with one variable

2X + 3Y = 2k-5, x-2y = - K + 7, and the value of X and 2Y are opposite to each other, find the value of K

The values of X and 2Y are opposite to each other,
Then x + 2Y = 0
x=-2y
2x+3y=2k-5,x-2y=-k+7
So, - 4Y + 3Y = 2k-5
-y=2k-5-----(1)
-2y-2y=-k+7
-4y=-k+7-----(2)
K = 3 can be obtained by solving binary linear equations

Solve the equation and find the unknown X. x × (3 / 1-8) = 5 / 3, 3 / 5 × (7 / 2-x) = 7 / 5

X × (3 / 1-8) = 5 / 3
5x/8=5/3
x=8/3
3 / 5 × (7 / 2-x) = 7 / 5
7/2-x=7/3
x=7/2-7/3
x=7/6

It is known that the equations of X and y are {2x + 3Y = 2k-5, x-2y = - K + 7, and the values of X and 2Y are opposite to each other

The opposite number is x = - 2Y
Substituting
-4y+3y=2k-5 (1)
-2y-2y=-k+7 (2)
So y = - 2K + 5
Substituting (2)
8k-20=-k+7
9k=27
k=3