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

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


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

Reorder the terms:
-2x(-1 + x) + 5x = 2(2x + -1)
(-1 * -2x + x * -2x) + 5x = 2(2x + -1)
(2x + -2x2) + 5x = 2(2x + -1)

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

Combine like terms: 2x + 5x = 7x
7x + -2x2 = 2(2x + -1)

Reorder the terms:
7x + -2x2 = 2(-1 + 2x)
7x + -2x2 = (-1 * 2 + 2x * 2)
7x + -2x2 = (-2 + 4x)

Solving
7x + -2x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
2 + 7x + -4x + -2x2 = -2 + 4x + 2 + -4x

Combine like terms: 7x + -4x = 3x
2 + 3x + -2x2 = -2 + 4x + 2 + -4x

Reorder the terms:
2 + 3x + -2x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
2 + 3x + -2x2 = 0 + 4x + -4x
2 + 3x + -2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
2 + 3x + -2x2 = 0

Factor a trinomial.
(2 + -1x)(1 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {2, -0.5}

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