(2x-1)(x-4)+(x-5)(x-5)-(x-4)(3x-4)=-11

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Solution for (2x-1)(x-4)+(x-5)(x-5)-(x-4)(3x-4)=-11 equation:


Simplifying
(2x + -1)(x + -4) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11

Reorder the terms:
(-1 + 2x)(x + -4) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11

Reorder the terms:
(-1 + 2x)(-4 + x) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11

Multiply (-1 + 2x) * (-4 + x)
(-1(-4 + x) + 2x * (-4 + x)) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11
((-4 * -1 + x * -1) + 2x * (-4 + x)) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11
((4 + -1x) + 2x * (-4 + x)) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11
(4 + -1x + (-4 * 2x + x * 2x)) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11
(4 + -1x + (-8x + 2x2)) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11

Combine like terms: -1x + -8x = -9x
(4 + -9x + 2x2) + (x + -5)(x + -5) + -1(x + -4)(3x + -4) = -11

Reorder the terms:
4 + -9x + 2x2 + (-5 + x)(x + -5) + -1(x + -4)(3x + -4) = -11

Reorder the terms:
4 + -9x + 2x2 + (-5 + x)(-5 + x) + -1(x + -4)(3x + -4) = -11

Multiply (-5 + x) * (-5 + x)
4 + -9x + 2x2 + (-5(-5 + x) + x(-5 + x)) + -1(x + -4)(3x + -4) = -11
4 + -9x + 2x2 + ((-5 * -5 + x * -5) + x(-5 + x)) + -1(x + -4)(3x + -4) = -11
4 + -9x + 2x2 + ((25 + -5x) + x(-5 + x)) + -1(x + -4)(3x + -4) = -11
4 + -9x + 2x2 + (25 + -5x + (-5 * x + x * x)) + -1(x + -4)(3x + -4) = -11
4 + -9x + 2x2 + (25 + -5x + (-5x + x2)) + -1(x + -4)(3x + -4) = -11

Combine like terms: -5x + -5x = -10x
4 + -9x + 2x2 + (25 + -10x + x2) + -1(x + -4)(3x + -4) = -11

Reorder the terms:
4 + -9x + 2x2 + 25 + -10x + x2 + -1(-4 + x)(3x + -4) = -11

Reorder the terms:
4 + -9x + 2x2 + 25 + -10x + x2 + -1(-4 + x)(-4 + 3x) = -11

Multiply (-4 + x) * (-4 + 3x)
4 + -9x + 2x2 + 25 + -10x + x2 + -1(-4(-4 + 3x) + x(-4 + 3x)) = -11
4 + -9x + 2x2 + 25 + -10x + x2 + -1((-4 * -4 + 3x * -4) + x(-4 + 3x)) = -11
4 + -9x + 2x2 + 25 + -10x + x2 + -1((16 + -12x) + x(-4 + 3x)) = -11
4 + -9x + 2x2 + 25 + -10x + x2 + -1(16 + -12x + (-4 * x + 3x * x)) = -11
4 + -9x + 2x2 + 25 + -10x + x2 + -1(16 + -12x + (-4x + 3x2)) = -11

Combine like terms: -12x + -4x = -16x
4 + -9x + 2x2 + 25 + -10x + x2 + -1(16 + -16x + 3x2) = -11
4 + -9x + 2x2 + 25 + -10x + x2 + (16 * -1 + -16x * -1 + 3x2 * -1) = -11
4 + -9x + 2x2 + 25 + -10x + x2 + (-16 + 16x + -3x2) = -11

Reorder the terms:
4 + 25 + -16 + -9x + -10x + 16x + 2x2 + x2 + -3x2 = -11

Combine like terms: 4 + 25 = 29
29 + -16 + -9x + -10x + 16x + 2x2 + x2 + -3x2 = -11

Combine like terms: 29 + -16 = 13
13 + -9x + -10x + 16x + 2x2 + x2 + -3x2 = -11

Combine like terms: -9x + -10x = -19x
13 + -19x + 16x + 2x2 + x2 + -3x2 = -11

Combine like terms: -19x + 16x = -3x
13 + -3x + 2x2 + x2 + -3x2 = -11

Combine like terms: 2x2 + x2 = 3x2
13 + -3x + 3x2 + -3x2 = -11

Combine like terms: 3x2 + -3x2 = 0
13 + -3x + 0 = -11
13 + -3x = -11

Solving
13 + -3x = -11

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + -3x = -11 + -13

Combine like terms: 13 + -13 = 0
0 + -3x = -11 + -13
-3x = -11 + -13

Combine like terms: -11 + -13 = -24
-3x = -24

Divide each side by '-3'.
x = 8

Simplifying
x = 8

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