(2x+5)(x-1)=12x

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Solution for (2x+5)(x-1)=12x equation: 


Simplifying
(2x + 5)(x + -1) = 12x

Reorder the terms:
(5 + 2x)(x + -1) = 12x

Reorder the terms:
(5 + 2x)(-1 + x) = 12x

Multiply (5 + 2x) * (-1 + x)
(5(-1 + x) + 2x * (-1 + x)) = 12x
((-1 * 5 + x * 5) + 2x * (-1 + x)) = 12x
((-5 + 5x) + 2x * (-1 + x)) = 12x
(-5 + 5x + (-1 * 2x + x * 2x)) = 12x
(-5 + 5x + (-2x + 2x2)) = 12x

Combine like terms: 5x + -2x = 3x
(-5 + 3x + 2x2) = 12x

Solving
-5 + 3x + 2x2 = 12x

Solving for variable 'x'.

Reorder the terms:
-5 + 3x + -12x + 2x2 = 12x + -12x

Combine like terms: 3x + -12x = -9x
-5 + -9x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-5 + -9x + 2x2 = 0

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


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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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 = {-0.5, 5}

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