6x(x-1)=35-7x

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Solution for 6x(x-1)=35-7x equation: 


Simplifying
6x(x + -1) = 35 + -7x

Reorder the terms:
6x(-1 + x) = 35 + -7x
(-1 * 6x + x * 6x) = 35 + -7x
(-6x + 6x2) = 35 + -7x

Solving
-6x + 6x2 = 35 + -7x

Solving for variable 'x'.

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

Combine like terms: -6x + 7x = 1x
-35 + 1x + 6x2 = 35 + -7x + -35 + 7x

Reorder the terms:
-35 + 1x + 6x2 = 35 + -35 + -7x + 7x

Combine like terms: 35 + -35 = 0
-35 + 1x + 6x2 = 0 + -7x + 7x
-35 + 1x + 6x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-35 + 1x + 6x2 = 0

Factor a trinomial.
(-5 + -2x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-2.5, 2.333333333}

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