(2x-5)(x-2)=6

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Solution for (2x-5)(x-2)=6 equation: 


Simplifying
(2x + -5)(x + -2) = 6

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

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

Multiply (-5 + 2x) * (-2 + x)
(-5(-2 + x) + 2x * (-2 + x)) = 6
((-2 * -5 + x * -5) + 2x * (-2 + x)) = 6
((10 + -5x) + 2x * (-2 + x)) = 6
(10 + -5x + (-2 * 2x + x * 2x)) = 6
(10 + -5x + (-4x + 2x2)) = 6

Combine like terms: -5x + -4x = -9x
(10 + -9x + 2x2) = 6

Solving
10 + -9x + 2x2 = 6

Solving for variable 'x'.

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

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

Combine like terms: 6 + -6 = 0
4 + -9x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.5, 4}

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