(-2x-5)(4x+6)=(-2x-5)(11x+1)

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Solution for (-2x-5)(4x+6)=(-2x-5)(11x+1) equation: 


Simplifying
(-2x + -5)(4x + 6) = (-2x + -5)(11x + 1)

Reorder the terms:
(-5 + -2x)(4x + 6) = (-2x + -5)(11x + 1)

Reorder the terms:
(-5 + -2x)(6 + 4x) = (-2x + -5)(11x + 1)

Multiply (-5 + -2x) * (6 + 4x)
(-5(6 + 4x) + -2x * (6 + 4x)) = (-2x + -5)(11x + 1)
((6 * -5 + 4x * -5) + -2x * (6 + 4x)) = (-2x + -5)(11x + 1)
((-30 + -20x) + -2x * (6 + 4x)) = (-2x + -5)(11x + 1)
(-30 + -20x + (6 * -2x + 4x * -2x)) = (-2x + -5)(11x + 1)
(-30 + -20x + (-12x + -8x2)) = (-2x + -5)(11x + 1)

Combine like terms: -20x + -12x = -32x
(-30 + -32x + -8x2) = (-2x + -5)(11x + 1)

Reorder the terms:
-30 + -32x + -8x2 = (-5 + -2x)(11x + 1)

Reorder the terms:
-30 + -32x + -8x2 = (-5 + -2x)(1 + 11x)

Multiply (-5 + -2x) * (1 + 11x)
-30 + -32x + -8x2 = (-5(1 + 11x) + -2x * (1 + 11x))
-30 + -32x + -8x2 = ((1 * -5 + 11x * -5) + -2x * (1 + 11x))
-30 + -32x + -8x2 = ((-5 + -55x) + -2x * (1 + 11x))
-30 + -32x + -8x2 = (-5 + -55x + (1 * -2x + 11x * -2x))
-30 + -32x + -8x2 = (-5 + -55x + (-2x + -22x2))

Combine like terms: -55x + -2x = -57x
-30 + -32x + -8x2 = (-5 + -57x + -22x2)

Solving
-30 + -32x + -8x2 = -5 + -57x + -22x2

Solving for variable 'x'.

Reorder the terms:
-30 + 5 + -32x + 57x + -8x2 + 22x2 = -5 + -57x + -22x2 + 5 + 57x + 22x2

Combine like terms: -30 + 5 = -25
-25 + -32x + 57x + -8x2 + 22x2 = -5 + -57x + -22x2 + 5 + 57x + 22x2

Combine like terms: -32x + 57x = 25x
-25 + 25x + -8x2 + 22x2 = -5 + -57x + -22x2 + 5 + 57x + 22x2

Combine like terms: -8x2 + 22x2 = 14x2
-25 + 25x + 14x2 = -5 + -57x + -22x2 + 5 + 57x + 22x2

Reorder the terms:
-25 + 25x + 14x2 = -5 + 5 + -57x + 57x + -22x2 + 22x2

Combine like terms: -5 + 5 = 0
-25 + 25x + 14x2 = 0 + -57x + 57x + -22x2 + 22x2
-25 + 25x + 14x2 = -57x + 57x + -22x2 + 22x2

Combine like terms: -57x + 57x = 0
-25 + 25x + 14x2 = 0 + -22x2 + 22x2
-25 + 25x + 14x2 = -22x2 + 22x2

Combine like terms: -22x2 + 22x2 = 0
-25 + 25x + 14x2 = 0

Factor a trinomial.
(-5 + -2x)(5 + -7x) = 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 '(5 + -7x)' equal to zero and attempt to solve:

Simplifying
5 + -7x = 0

Solving
5 + -7x = 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 + -7x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7x = 0 + -5
-7x = 0 + -5

Combine like terms: 0 + -5 = -5
-7x = -5

Divide each side by '-7'.
x = 0.7142857143

Simplifying
x = 0.7142857143
Solution
x = {-2.5, 0.7142857143}

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