x(3x-5)+(2x-4)=(5x+8)(x-5)

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Solution for x(3x-5)+(2x-4)=(5x+8)(x-5) equation: 


Simplifying
x(3x + -5) + (2x + -4) = (5x + 8)(x + -5)

Reorder the terms:
x(-5 + 3x) + (2x + -4) = (5x + 8)(x + -5)
(-5 * x + 3x * x) + (2x + -4) = (5x + 8)(x + -5)
(-5x + 3x2) + (2x + -4) = (5x + 8)(x + -5)

Reorder the terms:
-5x + 3x2 + (-4 + 2x) = (5x + 8)(x + -5)

Remove parenthesis around (-4 + 2x)
-5x + 3x2 + -4 + 2x = (5x + 8)(x + -5)

Reorder the terms:
-4 + -5x + 2x + 3x2 = (5x + 8)(x + -5)

Combine like terms: -5x + 2x = -3x
-4 + -3x + 3x2 = (5x + 8)(x + -5)

Reorder the terms:
-4 + -3x + 3x2 = (8 + 5x)(x + -5)

Reorder the terms:
-4 + -3x + 3x2 = (8 + 5x)(-5 + x)

Multiply (8 + 5x) * (-5 + x)
-4 + -3x + 3x2 = (8(-5 + x) + 5x * (-5 + x))
-4 + -3x + 3x2 = ((-5 * 8 + x * 8) + 5x * (-5 + x))
-4 + -3x + 3x2 = ((-40 + 8x) + 5x * (-5 + x))
-4 + -3x + 3x2 = (-40 + 8x + (-5 * 5x + x * 5x))
-4 + -3x + 3x2 = (-40 + 8x + (-25x + 5x2))

Combine like terms: 8x + -25x = -17x
-4 + -3x + 3x2 = (-40 + -17x + 5x2)

Solving
-4 + -3x + 3x2 = -40 + -17x + 5x2

Solving for variable 'x'.

Reorder the terms:
-4 + 40 + -3x + 17x + 3x2 + -5x2 = -40 + -17x + 5x2 + 40 + 17x + -5x2

Combine like terms: -4 + 40 = 36
36 + -3x + 17x + 3x2 + -5x2 = -40 + -17x + 5x2 + 40 + 17x + -5x2

Combine like terms: -3x + 17x = 14x
36 + 14x + 3x2 + -5x2 = -40 + -17x + 5x2 + 40 + 17x + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
36 + 14x + -2x2 = -40 + -17x + 5x2 + 40 + 17x + -5x2

Reorder the terms:
36 + 14x + -2x2 = -40 + 40 + -17x + 17x + 5x2 + -5x2

Combine like terms: -40 + 40 = 0
36 + 14x + -2x2 = 0 + -17x + 17x + 5x2 + -5x2
36 + 14x + -2x2 = -17x + 17x + 5x2 + -5x2

Combine like terms: -17x + 17x = 0
36 + 14x + -2x2 = 0 + 5x2 + -5x2
36 + 14x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
36 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 7x + -1x2) = 0

Factor a trinomial.
2((9 + -1x)(2 + x)) = 0

Ignore the factor 2.

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

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9

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 = {9, -2}

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