(2x+4)(x-2)+(x-2)(2x-5)=0

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Solution for (2x+4)(x-2)+(x-2)(2x-5)=0 equation: 


Simplifying
(2x + 4)(x + -2) + (x + -2)(2x + -5) = 0

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

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

Multiply (4 + 2x) * (-2 + x)
(4(-2 + x) + 2x * (-2 + x)) + (x + -2)(2x + -5) = 0
((-2 * 4 + x * 4) + 2x * (-2 + x)) + (x + -2)(2x + -5) = 0
((-8 + 4x) + 2x * (-2 + x)) + (x + -2)(2x + -5) = 0
(-8 + 4x + (-2 * 2x + x * 2x)) + (x + -2)(2x + -5) = 0
(-8 + 4x + (-4x + 2x2)) + (x + -2)(2x + -5) = 0

Combine like terms: 4x + -4x = 0
(-8 + 0 + 2x2) + (x + -2)(2x + -5) = 0
(-8 + 2x2) + (x + -2)(2x + -5) = 0

Reorder the terms:
-8 + 2x2 + (-2 + x)(2x + -5) = 0

Reorder the terms:
-8 + 2x2 + (-2 + x)(-5 + 2x) = 0

Multiply (-2 + x) * (-5 + 2x)
-8 + 2x2 + (-2(-5 + 2x) + x(-5 + 2x)) = 0
-8 + 2x2 + ((-5 * -2 + 2x * -2) + x(-5 + 2x)) = 0
-8 + 2x2 + ((10 + -4x) + x(-5 + 2x)) = 0
-8 + 2x2 + (10 + -4x + (-5 * x + 2x * x)) = 0
-8 + 2x2 + (10 + -4x + (-5x + 2x2)) = 0

Combine like terms: -4x + -5x = -9x
-8 + 2x2 + (10 + -9x + 2x2) = 0

Reorder the terms:
-8 + 10 + -9x + 2x2 + 2x2 = 0

Combine like terms: -8 + 10 = 2
2 + -9x + 2x2 + 2x2 = 0

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

Solving
2 + -9x + 4x2 = 0

Solving for variable 'x'.

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


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

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 = {0.25, 2}

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