(x-2)(2x-3)-(x+5)(2x+4)=0

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Solution for (x-2)(2x-3)-(x+5)(2x+4)=0 equation: 


Simplifying
(x + -2)(2x + -3) + -1(x + 5)(2x + 4) = 0

Reorder the terms:
(-2 + x)(2x + -3) + -1(x + 5)(2x + 4) = 0

Reorder the terms:
(-2 + x)(-3 + 2x) + -1(x + 5)(2x + 4) = 0

Multiply (-2 + x) * (-3 + 2x)
(-2(-3 + 2x) + x(-3 + 2x)) + -1(x + 5)(2x + 4) = 0
((-3 * -2 + 2x * -2) + x(-3 + 2x)) + -1(x + 5)(2x + 4) = 0
((6 + -4x) + x(-3 + 2x)) + -1(x + 5)(2x + 4) = 0
(6 + -4x + (-3 * x + 2x * x)) + -1(x + 5)(2x + 4) = 0
(6 + -4x + (-3x + 2x2)) + -1(x + 5)(2x + 4) = 0

Combine like terms: -4x + -3x = -7x
(6 + -7x + 2x2) + -1(x + 5)(2x + 4) = 0

Reorder the terms:
6 + -7x + 2x2 + -1(5 + x)(2x + 4) = 0

Reorder the terms:
6 + -7x + 2x2 + -1(5 + x)(4 + 2x) = 0

Multiply (5 + x) * (4 + 2x)
6 + -7x + 2x2 + -1(5(4 + 2x) + x(4 + 2x)) = 0
6 + -7x + 2x2 + -1((4 * 5 + 2x * 5) + x(4 + 2x)) = 0
6 + -7x + 2x2 + -1((20 + 10x) + x(4 + 2x)) = 0
6 + -7x + 2x2 + -1(20 + 10x + (4 * x + 2x * x)) = 0
6 + -7x + 2x2 + -1(20 + 10x + (4x + 2x2)) = 0

Combine like terms: 10x + 4x = 14x
6 + -7x + 2x2 + -1(20 + 14x + 2x2) = 0
6 + -7x + 2x2 + (20 * -1 + 14x * -1 + 2x2 * -1) = 0
6 + -7x + 2x2 + (-20 + -14x + -2x2) = 0

Reorder the terms:
6 + -20 + -7x + -14x + 2x2 + -2x2 = 0

Combine like terms: 6 + -20 = -14
-14 + -7x + -14x + 2x2 + -2x2 = 0

Combine like terms: -7x + -14x = -21x
-14 + -21x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
-14 + -21x + 0 = 0
-14 + -21x = 0

Solving
-14 + -21x = 0

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + -21x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -21x = 0 + 14
-21x = 0 + 14

Combine like terms: 0 + 14 = 14
-21x = 14

Divide each side by '-21'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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