((-2x)-6)(2x-5)=(2x-5)(9x+1)

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Solution for ((-2x)-6)(2x-5)=(2x-5)(9x+1) equation: 


Simplifying
((-2x) + -6)(2x + -5) = (2x + -5)(9x + 1)

Reorder the terms:
(-6 + (-2x))(2x + -5) = (2x + -5)(9x + 1)

Reorder the terms:
(-6 + (-2x))(-5 + 2x) = (2x + -5)(9x + 1)

Multiply (-6 + (-2x)) * (-5 + 2x)
(-6(-5 + 2x) + (-2x)(-5 + 2x)) = (2x + -5)(9x + 1)
((-5 * -6 + 2x * -6) + (-2x)(-5 + 2x)) = (2x + -5)(9x + 1)
((30 + -12x) + (-2x)(-5 + 2x)) = (2x + -5)(9x + 1)
(30 + -12x + (-5 * -2x + 2x * -2x)) = (2x + -5)(9x + 1)
(30 + -12x + (10x + -4x2)) = (2x + -5)(9x + 1)

Combine like terms: -12x + 10x = -2x
(30 + -2x + -4x2) = (2x + -5)(9x + 1)

Reorder the terms:
30 + -2x + -4x2 = (-5 + 2x)(9x + 1)

Reorder the terms:
30 + -2x + -4x2 = (-5 + 2x)(1 + 9x)

Multiply (-5 + 2x) * (1 + 9x)
30 + -2x + -4x2 = (-5(1 + 9x) + 2x * (1 + 9x))
30 + -2x + -4x2 = ((1 * -5 + 9x * -5) + 2x * (1 + 9x))
30 + -2x + -4x2 = ((-5 + -45x) + 2x * (1 + 9x))
30 + -2x + -4x2 = (-5 + -45x + (1 * 2x + 9x * 2x))
30 + -2x + -4x2 = (-5 + -45x + (2x + 18x2))

Combine like terms: -45x + 2x = -43x
30 + -2x + -4x2 = (-5 + -43x + 18x2)

Solving
30 + -2x + -4x2 = -5 + -43x + 18x2

Solving for variable 'x'.

Reorder the terms:
30 + 5 + -2x + 43x + -4x2 + -18x2 = -5 + -43x + 18x2 + 5 + 43x + -18x2

Combine like terms: 30 + 5 = 35
35 + -2x + 43x + -4x2 + -18x2 = -5 + -43x + 18x2 + 5 + 43x + -18x2

Combine like terms: -2x + 43x = 41x
35 + 41x + -4x2 + -18x2 = -5 + -43x + 18x2 + 5 + 43x + -18x2

Combine like terms: -4x2 + -18x2 = -22x2
35 + 41x + -22x2 = -5 + -43x + 18x2 + 5 + 43x + -18x2

Reorder the terms:
35 + 41x + -22x2 = -5 + 5 + -43x + 43x + 18x2 + -18x2

Combine like terms: -5 + 5 = 0
35 + 41x + -22x2 = 0 + -43x + 43x + 18x2 + -18x2
35 + 41x + -22x2 = -43x + 43x + 18x2 + -18x2

Combine like terms: -43x + 43x = 0
35 + 41x + -22x2 = 0 + 18x2 + -18x2
35 + 41x + -22x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
35 + 41x + -22x2 = 0

Factor a trinomial.
(5 + -2x)(7 + 11x) = 0


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(7 + 11x)' equal to zero and attempt to solve:

Simplifying
7 + 11x = 0

Solving
7 + 11x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 11x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 11x = 0 + -7
11x = 0 + -7

Combine like terms: 0 + -7 = -7
11x = -7

Divide each side by '11'.
x = -0.6363636364

Simplifying
x = -0.6363636364
Solution
x = {2.5, -0.6363636364}

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