6x(x-5)+7(x-5)=0

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Solution for 6x(x-5)+7(x-5)=0 equation: 


Simplifying
6x(x + -5) + 7(x + -5) = 0

Reorder the terms:
6x(-5 + x) + 7(x + -5) = 0
(-5 * 6x + x * 6x) + 7(x + -5) = 0
(-30x + 6x2) + 7(x + -5) = 0

Reorder the terms:
-30x + 6x2 + 7(-5 + x) = 0
-30x + 6x2 + (-5 * 7 + x * 7) = 0
-30x + 6x2 + (-35 + 7x) = 0

Reorder the terms:
-35 + -30x + 7x + 6x2 = 0

Combine like terms: -30x + 7x = -23x
-35 + -23x + 6x2 = 0

Solving
-35 + -23x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -6x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve:

Simplifying
-7 + -6x = 0

Solving
-7 + -6x = 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 + -6x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6x = 0 + 7
-6x = 0 + 7

Combine like terms: 0 + 7 = 7
-6x = 7

Divide each side by '-6'.
x = -1.166666667

Simplifying
x = -1.166666667

Subproblem 2
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
Solution
x = {-1.166666667, 5}

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