(1-2x)(x-11)=(4x-5)(x+7)

Solution for (1-2x)(x-11)=(4x-5)(x+7) equation:

Simplifying
(1 + -2x)(x + -11) = (4x + -5)(x + 7)

Reorder the terms:
(1 + -2x)(-11 + x) = (4x + -5)(x + 7)

Multiply (1 + -2x) * (-11 + x)
(1(-11 + x) + -2x * (-11 + x)) = (4x + -5)(x + 7)
((-11 * 1 + x * 1) + -2x * (-11 + x)) = (4x + -5)(x + 7)
((-11 + 1x) + -2x * (-11 + x)) = (4x + -5)(x + 7)
(-11 + 1x + (-11 * -2x + x * -2x)) = (4x + -5)(x + 7)
(-11 + 1x + (22x + -2x2)) = (4x + -5)(x + 7)

Combine like terms: 1x + 22x = 23x
(-11 + 23x + -2x2) = (4x + -5)(x + 7)

Reorder the terms:
-11 + 23x + -2x2 = (-5 + 4x)(x + 7)

Reorder the terms:
-11 + 23x + -2x2 = (-5 + 4x)(7 + x)

Multiply (-5 + 4x) * (7 + x)
-11 + 23x + -2x2 = (-5(7 + x) + 4x * (7 + x))
-11 + 23x + -2x2 = ((7 * -5 + x * -5) + 4x * (7 + x))
-11 + 23x + -2x2 = ((-35 + -5x) + 4x * (7 + x))
-11 + 23x + -2x2 = (-35 + -5x + (7 * 4x + x * 4x))
-11 + 23x + -2x2 = (-35 + -5x + (28x + 4x2))

Combine like terms: -5x + 28x = 23x
-11 + 23x + -2x2 = (-35 + 23x + 4x2)

Add '-23x' to each side of the equation.
-11 + 23x + -23x + -2x2 = -35 + 23x + -23x + 4x2

Combine like terms: 23x + -23x = 0
-11 + 0 + -2x2 = -35 + 23x + -23x + 4x2
-11 + -2x2 = -35 + 23x + -23x + 4x2

Combine like terms: 23x + -23x = 0
-11 + -2x2 = -35 + 0 + 4x2
-11 + -2x2 = -35 + 4x2

Solving
-11 + -2x2 = -35 + 4x2

Solving for variable 'x'.

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

Add '-4x2' to each side of the equation.
-11 + -2x2 + -4x2 = -35 + 4x2 + -4x2

Combine like terms: -2x2 + -4x2 = -6x2
-11 + -6x2 = -35 + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-11 + -6x2 = -35 + 0
-11 + -6x2 = -35

Add '11' to each side of the equation.
-11 + 11 + -6x2 = -35 + 11

Combine like terms: -11 + 11 = 0
0 + -6x2 = -35 + 11
-6x2 = -35 + 11

Combine like terms: -35 + 11 = -24
-6x2 = -24

Divide each side by '-6'.
x2 = 4

Simplifying
x2 = 4

Take the square root of each side:
x = {-2, 2}