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

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


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

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

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

Multiply (1 + 2x) * (2 + 5x)
(1(2 + 5x) + 2x * (2 + 5x)) = (2x + -2)(x + -2)
((2 * 1 + 5x * 1) + 2x * (2 + 5x)) = (2x + -2)(x + -2)
((2 + 5x) + 2x * (2 + 5x)) = (2x + -2)(x + -2)
(2 + 5x + (2 * 2x + 5x * 2x)) = (2x + -2)(x + -2)
(2 + 5x + (4x + 10x2)) = (2x + -2)(x + -2)

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

Reorder the terms:
2 + 9x + 10x2 = (-2 + 2x)(x + -2)

Reorder the terms:
2 + 9x + 10x2 = (-2 + 2x)(-2 + x)

Multiply (-2 + 2x) * (-2 + x)
2 + 9x + 10x2 = (-2(-2 + x) + 2x * (-2 + x))
2 + 9x + 10x2 = ((-2 * -2 + x * -2) + 2x * (-2 + x))
2 + 9x + 10x2 = ((4 + -2x) + 2x * (-2 + x))
2 + 9x + 10x2 = (4 + -2x + (-2 * 2x + x * 2x))
2 + 9x + 10x2 = (4 + -2x + (-4x + 2x2))

Combine like terms: -2x + -4x = -6x
2 + 9x + 10x2 = (4 + -6x + 2x2)

Solving
2 + 9x + 10x2 = 4 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + -4 + 9x + 6x + 10x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Combine like terms: 2 + -4 = -2
-2 + 9x + 6x + 10x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Combine like terms: 9x + 6x = 15x
-2 + 15x + 10x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Combine like terms: 10x2 + -2x2 = 8x2
-2 + 15x + 8x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2

Reorder the terms:
-2 + 15x + 8x2 = 4 + -4 + -6x + 6x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-2 + 15x + 8x2 = 0 + -6x + 6x + 2x2 + -2x2
-2 + 15x + 8x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-2 + 15x + 8x2 = 0 + 2x2 + -2x2
-2 + 15x + 8x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2 + 15x + 8x2 = 0

Factor a trinomial.
(-2 + -1x)(1 + -8x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + -8x)' equal to zero and attempt to solve:

Simplifying
1 + -8x = 0

Solving
1 + -8x = 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 + -8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8x = 0 + -1
-8x = 0 + -1

Combine like terms: 0 + -1 = -1
-8x = -1

Divide each side by '-8'.
x = 0.125

Simplifying
x = 0.125
Solution
x = {-2, 0.125}

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