(x+3)(3x-5)=5(x+1)-10

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Solution for (x+3)(3x-5)=5(x+1)-10 equation: 


Simplifying
(x + 3)(3x + -5) = 5(x + 1) + -10

Reorder the terms:
(3 + x)(3x + -5) = 5(x + 1) + -10

Reorder the terms:
(3 + x)(-5 + 3x) = 5(x + 1) + -10

Multiply (3 + x) * (-5 + 3x)
(3(-5 + 3x) + x(-5 + 3x)) = 5(x + 1) + -10
((-5 * 3 + 3x * 3) + x(-5 + 3x)) = 5(x + 1) + -10
((-15 + 9x) + x(-5 + 3x)) = 5(x + 1) + -10
(-15 + 9x + (-5 * x + 3x * x)) = 5(x + 1) + -10
(-15 + 9x + (-5x + 3x2)) = 5(x + 1) + -10

Combine like terms: 9x + -5x = 4x
(-15 + 4x + 3x2) = 5(x + 1) + -10

Reorder the terms:
-15 + 4x + 3x2 = 5(1 + x) + -10
-15 + 4x + 3x2 = (1 * 5 + x * 5) + -10
-15 + 4x + 3x2 = (5 + 5x) + -10

Reorder the terms:
-15 + 4x + 3x2 = 5 + -10 + 5x

Combine like terms: 5 + -10 = -5
-15 + 4x + 3x2 = -5 + 5x

Solving
-15 + 4x + 3x2 = -5 + 5x

Solving for variable 'x'.

Reorder the terms:
-15 + 5 + 4x + -5x + 3x2 = -5 + 5x + 5 + -5x

Combine like terms: -15 + 5 = -10
-10 + 4x + -5x + 3x2 = -5 + 5x + 5 + -5x

Combine like terms: 4x + -5x = -1x
-10 + -1x + 3x2 = -5 + 5x + 5 + -5x

Reorder the terms:
-10 + -1x + 3x2 = -5 + 5 + 5x + -5x

Combine like terms: -5 + 5 = 0
-10 + -1x + 3x2 = 0 + 5x + -5x
-10 + -1x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-10 + -1x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 2}

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