(3x-2)(2x-5)=2(3x+4)(x-1)-45

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Solution for (3x-2)(2x-5)=2(3x+4)(x-1)-45 equation: 


Simplifying
(3x + -2)(2x + -5) = 2(3x + 4)(x + -1) + -45

Reorder the terms:
(-2 + 3x)(2x + -5) = 2(3x + 4)(x + -1) + -45

Reorder the terms:
(-2 + 3x)(-5 + 2x) = 2(3x + 4)(x + -1) + -45

Multiply (-2 + 3x) * (-5 + 2x)
(-2(-5 + 2x) + 3x * (-5 + 2x)) = 2(3x + 4)(x + -1) + -45
((-5 * -2 + 2x * -2) + 3x * (-5 + 2x)) = 2(3x + 4)(x + -1) + -45
((10 + -4x) + 3x * (-5 + 2x)) = 2(3x + 4)(x + -1) + -45
(10 + -4x + (-5 * 3x + 2x * 3x)) = 2(3x + 4)(x + -1) + -45
(10 + -4x + (-15x + 6x2)) = 2(3x + 4)(x + -1) + -45

Combine like terms: -4x + -15x = -19x
(10 + -19x + 6x2) = 2(3x + 4)(x + -1) + -45

Reorder the terms:
10 + -19x + 6x2 = 2(4 + 3x)(x + -1) + -45

Reorder the terms:
10 + -19x + 6x2 = 2(4 + 3x)(-1 + x) + -45

Multiply (4 + 3x) * (-1 + x)
10 + -19x + 6x2 = 2(4(-1 + x) + 3x * (-1 + x)) + -45
10 + -19x + 6x2 = 2((-1 * 4 + x * 4) + 3x * (-1 + x)) + -45
10 + -19x + 6x2 = 2((-4 + 4x) + 3x * (-1 + x)) + -45
10 + -19x + 6x2 = 2(-4 + 4x + (-1 * 3x + x * 3x)) + -45
10 + -19x + 6x2 = 2(-4 + 4x + (-3x + 3x2)) + -45

Combine like terms: 4x + -3x = 1x
10 + -19x + 6x2 = 2(-4 + 1x + 3x2) + -45
10 + -19x + 6x2 = (-4 * 2 + 1x * 2 + 3x2 * 2) + -45
10 + -19x + 6x2 = (-8 + 2x + 6x2) + -45

Reorder the terms:
10 + -19x + 6x2 = -8 + -45 + 2x + 6x2

Combine like terms: -8 + -45 = -53
10 + -19x + 6x2 = -53 + 2x + 6x2

Add '-6x2' to each side of the equation.
10 + -19x + 6x2 + -6x2 = -53 + 2x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
10 + -19x + 0 = -53 + 2x + 6x2 + -6x2
10 + -19x = -53 + 2x + 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
10 + -19x = -53 + 2x + 0
10 + -19x = -53 + 2x

Solving
10 + -19x = -53 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
10 + -19x + -2x = -53 + 2x + -2x

Combine like terms: -19x + -2x = -21x
10 + -21x = -53 + 2x + -2x

Combine like terms: 2x + -2x = 0
10 + -21x = -53 + 0
10 + -21x = -53

Add '-10' to each side of the equation.
10 + -10 + -21x = -53 + -10

Combine like terms: 10 + -10 = 0
0 + -21x = -53 + -10
-21x = -53 + -10

Combine like terms: -53 + -10 = -63
-21x = -63

Divide each side by '-21'.
x = 3

Simplifying
x = 3

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