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

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Solution for (2*x+1)(2x+1)-(3*x-2)(3x-2)+(5*x-1)*(4*x+5)=0 equation: 


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

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

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

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

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

Reorder the terms:
1 + 4x + 4x2 + -1(-2 + 3x)(3x + -2) + (5x + -1)(4x + 5) = 0

Reorder the terms:
1 + 4x + 4x2 + -1(-2 + 3x)(-2 + 3x) + (5x + -1)(4x + 5) = 0

Multiply (-2 + 3x) * (-2 + 3x)
1 + 4x + 4x2 + -1(-2(-2 + 3x) + 3x * (-2 + 3x)) + (5x + -1)(4x + 5) = 0
1 + 4x + 4x2 + -1((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) + (5x + -1)(4x + 5) = 0
1 + 4x + 4x2 + -1((4 + -6x) + 3x * (-2 + 3x)) + (5x + -1)(4x + 5) = 0
1 + 4x + 4x2 + -1(4 + -6x + (-2 * 3x + 3x * 3x)) + (5x + -1)(4x + 5) = 0
1 + 4x + 4x2 + -1(4 + -6x + (-6x + 9x2)) + (5x + -1)(4x + 5) = 0

Combine like terms: -6x + -6x = -12x
1 + 4x + 4x2 + -1(4 + -12x + 9x2) + (5x + -1)(4x + 5) = 0
1 + 4x + 4x2 + (4 * -1 + -12x * -1 + 9x2 * -1) + (5x + -1)(4x + 5) = 0
1 + 4x + 4x2 + (-4 + 12x + -9x2) + (5x + -1)(4x + 5) = 0

Reorder the terms:
1 + 4x + 4x2 + -4 + 12x + -9x2 + (-1 + 5x)(4x + 5) = 0

Reorder the terms:
1 + 4x + 4x2 + -4 + 12x + -9x2 + (-1 + 5x)(5 + 4x) = 0

Multiply (-1 + 5x) * (5 + 4x)
1 + 4x + 4x2 + -4 + 12x + -9x2 + (-1(5 + 4x) + 5x * (5 + 4x)) = 0
1 + 4x + 4x2 + -4 + 12x + -9x2 + ((5 * -1 + 4x * -1) + 5x * (5 + 4x)) = 0
1 + 4x + 4x2 + -4 + 12x + -9x2 + ((-5 + -4x) + 5x * (5 + 4x)) = 0
1 + 4x + 4x2 + -4 + 12x + -9x2 + (-5 + -4x + (5 * 5x + 4x * 5x)) = 0
1 + 4x + 4x2 + -4 + 12x + -9x2 + (-5 + -4x + (25x + 20x2)) = 0

Combine like terms: -4x + 25x = 21x
1 + 4x + 4x2 + -4 + 12x + -9x2 + (-5 + 21x + 20x2) = 0

Reorder the terms:
1 + -4 + -5 + 4x + 12x + 21x + 4x2 + -9x2 + 20x2 = 0

Combine like terms: 1 + -4 = -3
-3 + -5 + 4x + 12x + 21x + 4x2 + -9x2 + 20x2 = 0

Combine like terms: -3 + -5 = -8
-8 + 4x + 12x + 21x + 4x2 + -9x2 + 20x2 = 0

Combine like terms: 4x + 12x = 16x
-8 + 16x + 21x + 4x2 + -9x2 + 20x2 = 0

Combine like terms: 16x + 21x = 37x
-8 + 37x + 4x2 + -9x2 + 20x2 = 0

Combine like terms: 4x2 + -9x2 = -5x2
-8 + 37x + -5x2 + 20x2 = 0

Combine like terms: -5x2 + 20x2 = 15x2
-8 + 37x + 15x2 = 0

Solving
-8 + 37x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -3x)(1 + -5x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-2.666666667, 0.2}

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