2x(x-2)+5(x-2)=0

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Solution for 2x(x-2)+5(x-2)=0 equation: 


Simplifying
2x(x + -2) + 5(x + -2) = 0

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

Reorder the terms:
-4x + 2x2 + 5(-2 + x) = 0
-4x + 2x2 + (-2 * 5 + x * 5) = 0
-4x + 2x2 + (-10 + 5x) = 0

Reorder the terms:
-10 + -4x + 5x + 2x2 = 0

Combine like terms: -4x + 5x = 1x
-10 + 1x + 2x2 = 0

Solving
-10 + 1x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(2 + -1x) = 0


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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
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
Solution
x = {-2.5, 2}

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