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

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


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

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

Reorder the terms for easier multiplication:
5x(-5 + 3x) + (3x + -5) * 7 = 0
(-5 * 5x + 3x * 5x) + (3x + -5) * 7 = 0
(-25x + 15x2) + (3x + -5) * 7 = 0

Reorder the terms:
-25x + 15x2 + (-5 + 3x) * 7 = 0

Reorder the terms for easier multiplication:
-25x + 15x2 + 7(-5 + 3x) = 0
-25x + 15x2 + (-5 * 7 + 3x * 7) = 0
-25x + 15x2 + (-35 + 21x) = 0

Reorder the terms:
-35 + -25x + 21x + 15x2 = 0

Combine like terms: -25x + 21x = -4x
-35 + -4x + 15x2 = 0

Solving
-35 + -4x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -5x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve:

Simplifying
-7 + -5x = 0

Solving
-7 + -5x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5x = 0 + 7
-5x = 0 + 7

Combine like terms: 0 + 7 = 7
-5x = 7

Divide each side by '-5'.
x = -1.4

Simplifying
x = -1.4

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 = {-1.4, 1.666666667}

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