(4x-3)(3x-2)=(2x-13)(x-2)+20

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Solution for (4x-3)(3x-2)=(2x-13)(x-2)+20 equation:


Simplifying
(4x + -3)(3x + -2) = (2x + -13)(x + -2) + 20

Reorder the terms:
(-3 + 4x)(3x + -2) = (2x + -13)(x + -2) + 20

Reorder the terms:
(-3 + 4x)(-2 + 3x) = (2x + -13)(x + -2) + 20

Multiply (-3 + 4x) * (-2 + 3x)
(-3(-2 + 3x) + 4x * (-2 + 3x)) = (2x + -13)(x + -2) + 20
((-2 * -3 + 3x * -3) + 4x * (-2 + 3x)) = (2x + -13)(x + -2) + 20
((6 + -9x) + 4x * (-2 + 3x)) = (2x + -13)(x + -2) + 20
(6 + -9x + (-2 * 4x + 3x * 4x)) = (2x + -13)(x + -2) + 20
(6 + -9x + (-8x + 12x2)) = (2x + -13)(x + -2) + 20

Combine like terms: -9x + -8x = -17x
(6 + -17x + 12x2) = (2x + -13)(x + -2) + 20

Reorder the terms:
6 + -17x + 12x2 = (-13 + 2x)(x + -2) + 20

Reorder the terms:
6 + -17x + 12x2 = (-13 + 2x)(-2 + x) + 20

Multiply (-13 + 2x) * (-2 + x)
6 + -17x + 12x2 = (-13(-2 + x) + 2x * (-2 + x)) + 20
6 + -17x + 12x2 = ((-2 * -13 + x * -13) + 2x * (-2 + x)) + 20
6 + -17x + 12x2 = ((26 + -13x) + 2x * (-2 + x)) + 20
6 + -17x + 12x2 = (26 + -13x + (-2 * 2x + x * 2x)) + 20
6 + -17x + 12x2 = (26 + -13x + (-4x + 2x2)) + 20

Combine like terms: -13x + -4x = -17x
6 + -17x + 12x2 = (26 + -17x + 2x2) + 20

Reorder the terms:
6 + -17x + 12x2 = 26 + 20 + -17x + 2x2

Combine like terms: 26 + 20 = 46
6 + -17x + 12x2 = 46 + -17x + 2x2

Add '17x' to each side of the equation.
6 + -17x + 17x + 12x2 = 46 + -17x + 17x + 2x2

Combine like terms: -17x + 17x = 0
6 + 0 + 12x2 = 46 + -17x + 17x + 2x2
6 + 12x2 = 46 + -17x + 17x + 2x2

Combine like terms: -17x + 17x = 0
6 + 12x2 = 46 + 0 + 2x2
6 + 12x2 = 46 + 2x2

Solving
6 + 12x2 = 46 + 2x2

Solving for variable 'x'.

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

Add '-2x2' to each side of the equation.
6 + 12x2 + -2x2 = 46 + 2x2 + -2x2

Combine like terms: 12x2 + -2x2 = 10x2
6 + 10x2 = 46 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + 10x2 = 46 + 0
6 + 10x2 = 46

Add '-6' to each side of the equation.
6 + -6 + 10x2 = 46 + -6

Combine like terms: 6 + -6 = 0
0 + 10x2 = 46 + -6
10x2 = 46 + -6

Combine like terms: 46 + -6 = 40
10x2 = 40

Divide each side by '10'.
x2 = 4

Simplifying
x2 = 4

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

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