(2x+5)(x-3)=6x

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Solution for (2x+5)(x-3)=6x equation: 


Simplifying
(2x + 5)(x + -3) = 6x

Reorder the terms:
(5 + 2x)(x + -3) = 6x

Reorder the terms:
(5 + 2x)(-3 + x) = 6x

Multiply (5 + 2x) * (-3 + x)
(5(-3 + x) + 2x * (-3 + x)) = 6x
((-3 * 5 + x * 5) + 2x * (-3 + x)) = 6x
((-15 + 5x) + 2x * (-3 + x)) = 6x
(-15 + 5x + (-3 * 2x + x * 2x)) = 6x
(-15 + 5x + (-6x + 2x2)) = 6x

Combine like terms: 5x + -6x = -1x
(-15 + -1x + 2x2) = 6x

Solving
-15 + -1x + 2x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-15 + -1x + -6x + 2x2 = 6x + -6x

Combine like terms: -1x + -6x = -7x
-15 + -7x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-15 + -7x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 5}

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