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

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


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

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

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

Multiply (-5 + 2x) * (4 + 5x)
(-5(4 + 5x) + 2x * (4 + 5x)) = (2x + -1)(4x + -1)
((4 * -5 + 5x * -5) + 2x * (4 + 5x)) = (2x + -1)(4x + -1)
((-20 + -25x) + 2x * (4 + 5x)) = (2x + -1)(4x + -1)
(-20 + -25x + (4 * 2x + 5x * 2x)) = (2x + -1)(4x + -1)
(-20 + -25x + (8x + 10x2)) = (2x + -1)(4x + -1)

Combine like terms: -25x + 8x = -17x
(-20 + -17x + 10x2) = (2x + -1)(4x + -1)

Reorder the terms:
-20 + -17x + 10x2 = (-1 + 2x)(4x + -1)

Reorder the terms:
-20 + -17x + 10x2 = (-1 + 2x)(-1 + 4x)

Multiply (-1 + 2x) * (-1 + 4x)
-20 + -17x + 10x2 = (-1(-1 + 4x) + 2x * (-1 + 4x))
-20 + -17x + 10x2 = ((-1 * -1 + 4x * -1) + 2x * (-1 + 4x))
-20 + -17x + 10x2 = ((1 + -4x) + 2x * (-1 + 4x))
-20 + -17x + 10x2 = (1 + -4x + (-1 * 2x + 4x * 2x))
-20 + -17x + 10x2 = (1 + -4x + (-2x + 8x2))

Combine like terms: -4x + -2x = -6x
-20 + -17x + 10x2 = (1 + -6x + 8x2)

Solving
-20 + -17x + 10x2 = 1 + -6x + 8x2

Solving for variable 'x'.

Reorder the terms:
-20 + -1 + -17x + 6x + 10x2 + -8x2 = 1 + -6x + 8x2 + -1 + 6x + -8x2

Combine like terms: -20 + -1 = -21
-21 + -17x + 6x + 10x2 + -8x2 = 1 + -6x + 8x2 + -1 + 6x + -8x2

Combine like terms: -17x + 6x = -11x
-21 + -11x + 10x2 + -8x2 = 1 + -6x + 8x2 + -1 + 6x + -8x2

Combine like terms: 10x2 + -8x2 = 2x2
-21 + -11x + 2x2 = 1 + -6x + 8x2 + -1 + 6x + -8x2

Reorder the terms:
-21 + -11x + 2x2 = 1 + -1 + -6x + 6x + 8x2 + -8x2

Combine like terms: 1 + -1 = 0
-21 + -11x + 2x2 = 0 + -6x + 6x + 8x2 + -8x2
-21 + -11x + 2x2 = -6x + 6x + 8x2 + -8x2

Combine like terms: -6x + 6x = 0
-21 + -11x + 2x2 = 0 + 8x2 + -8x2
-21 + -11x + 2x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-21 + -11x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.5, 7}

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