(x+5)(x+2)=(x+2)(3x-4)

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Solution for (x+5)(x+2)=(x+2)(3x-4) equation: 


Simplifying
(x + 5)(x + 2) = (x + 2)(3x + -4)

Reorder the terms:
(5 + x)(x + 2) = (x + 2)(3x + -4)

Reorder the terms:
(5 + x)(2 + x) = (x + 2)(3x + -4)

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = (x + 2)(3x + -4)
((2 * 5 + x * 5) + x(2 + x)) = (x + 2)(3x + -4)
((10 + 5x) + x(2 + x)) = (x + 2)(3x + -4)
(10 + 5x + (2 * x + x * x)) = (x + 2)(3x + -4)
(10 + 5x + (2x + x2)) = (x + 2)(3x + -4)

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = (x + 2)(3x + -4)

Reorder the terms:
10 + 7x + x2 = (2 + x)(3x + -4)

Reorder the terms:
10 + 7x + x2 = (2 + x)(-4 + 3x)

Multiply (2 + x) * (-4 + 3x)
10 + 7x + x2 = (2(-4 + 3x) + x(-4 + 3x))
10 + 7x + x2 = ((-4 * 2 + 3x * 2) + x(-4 + 3x))
10 + 7x + x2 = ((-8 + 6x) + x(-4 + 3x))
10 + 7x + x2 = (-8 + 6x + (-4 * x + 3x * x))
10 + 7x + x2 = (-8 + 6x + (-4x + 3x2))

Combine like terms: 6x + -4x = 2x
10 + 7x + x2 = (-8 + 2x + 3x2)

Solving
10 + 7x + x2 = -8 + 2x + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + 8 + 7x + -2x + x2 + -3x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Combine like terms: 10 + 8 = 18
18 + 7x + -2x + x2 + -3x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Combine like terms: 7x + -2x = 5x
18 + 5x + x2 + -3x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Combine like terms: x2 + -3x2 = -2x2
18 + 5x + -2x2 = -8 + 2x + 3x2 + 8 + -2x + -3x2

Reorder the terms:
18 + 5x + -2x2 = -8 + 8 + 2x + -2x + 3x2 + -3x2

Combine like terms: -8 + 8 = 0
18 + 5x + -2x2 = 0 + 2x + -2x + 3x2 + -3x2
18 + 5x + -2x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
18 + 5x + -2x2 = 0 + 3x2 + -3x2
18 + 5x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
18 + 5x + -2x2 = 0

Factor a trinomial.
(9 + -2x)(2 + x) = 0


Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

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

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

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {4.5, -2}

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