-6x(x-3)=7x+5

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Solution for -6x(x-3)=7x+5 equation: 


Simplifying
-6x(x + -3) = 7x + 5

Reorder the terms:
-6x(-3 + x) = 7x + 5
(-3 * -6x + x * -6x) = 7x + 5
(18x + -6x2) = 7x + 5

Reorder the terms:
18x + -6x2 = 5 + 7x

Solving
18x + -6x2 = 5 + 7x

Solving for variable 'x'.

Reorder the terms:
-5 + 18x + -7x + -6x2 = 5 + 7x + -5 + -7x

Combine like terms: 18x + -7x = 11x
-5 + 11x + -6x2 = 5 + 7x + -5 + -7x

Reorder the terms:
-5 + 11x + -6x2 = 5 + -5 + 7x + -7x

Combine like terms: 5 + -5 = 0
-5 + 11x + -6x2 = 0 + 7x + -7x
-5 + 11x + -6x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-5 + 11x + -6x2 = 0

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


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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {1, 0.8333333333}

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