11x(x-2)=22-2(7x-3)

Solution for 11x(x-2)=22-2(7x-3) equation:

Simplifying
11x(x + -2) = 22 + -2(7x + -3)

Reorder the terms:
11x(-2 + x) = 22 + -2(7x + -3)
(-2 * 11x + x * 11x) = 22 + -2(7x + -3)
(-22x + 11x2) = 22 + -2(7x + -3)

Reorder the terms:
-22x + 11x2 = 22 + -2(-3 + 7x)
-22x + 11x2 = 22 + (-3 * -2 + 7x * -2)
-22x + 11x2 = 22 + (6 + -14x)

Combine like terms: 22 + 6 = 28
-22x + 11x2 = 28 + -14x

Solving
-22x + 11x2 = 28 + -14x

Solving for variable 'x'.

Reorder the terms:
-28 + -22x + 14x + 11x2 = 28 + -14x + -28 + 14x

Combine like terms: -22x + 14x = -8x
-28 + -8x + 11x2 = 28 + -14x + -28 + 14x

Reorder the terms:
-28 + -8x + 11x2 = 28 + -28 + -14x + 14x

Combine like terms: 28 + -28 = 0
-28 + -8x + 11x2 = 0 + -14x + 14x
-28 + -8x + 11x2 = -14x + 14x

Combine like terms: -14x + 14x = 0
-28 + -8x + 11x2 = 0

Factor a trinomial.
(-14 + -11x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -11x)' equal to zero and attempt to solve:

Simplifying
-14 + -11x = 0

Solving
-14 + -11x = 0

Move all terms containing x to the left, all other terms to the right.

Add '14' to each side of the equation.
-14 + 14 + -11x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -11x = 0 + 14
-11x = 0 + 14

Combine like terms: 0 + 14 = 14
-11x = 14

Divide each side by '-11'.
x = -1.272727273

Simplifying
x = -1.272727273
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.272727273, 2}