-2(3x-5)+(x+7)(3x-5)=0

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Solution for -2(3x-5)+(x+7)(3x-5)=0 equation: 


Simplifying
-2(3x + -5) + (x + 7)(3x + -5) = 0

Reorder the terms:
-2(-5 + 3x) + (x + 7)(3x + -5) = 0
(-5 * -2 + 3x * -2) + (x + 7)(3x + -5) = 0
(10 + -6x) + (x + 7)(3x + -5) = 0

Reorder the terms:
10 + -6x + (7 + x)(3x + -5) = 0

Reorder the terms:
10 + -6x + (7 + x)(-5 + 3x) = 0

Multiply (7 + x) * (-5 + 3x)
10 + -6x + (7(-5 + 3x) + x(-5 + 3x)) = 0
10 + -6x + ((-5 * 7 + 3x * 7) + x(-5 + 3x)) = 0
10 + -6x + ((-35 + 21x) + x(-5 + 3x)) = 0
10 + -6x + (-35 + 21x + (-5 * x + 3x * x)) = 0
10 + -6x + (-35 + 21x + (-5x + 3x2)) = 0

Combine like terms: 21x + -5x = 16x
10 + -6x + (-35 + 16x + 3x2) = 0

Reorder the terms:
10 + -35 + -6x + 16x + 3x2 = 0

Combine like terms: 10 + -35 = -25
-25 + -6x + 16x + 3x2 = 0

Combine like terms: -6x + 16x = 10x
-25 + 10x + 3x2 = 0

Solving
-25 + 10x + 3x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, 1.666666667}

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