2x(x-1)=5(x+3)

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Solution for 2x(x-1)=5(x+3) equation: 


Simplifying
2x(x + -1) = 5(x + 3)

Reorder the terms:
2x(-1 + x) = 5(x + 3)
(-1 * 2x + x * 2x) = 5(x + 3)
(-2x + 2x2) = 5(x + 3)

Reorder the terms:
-2x + 2x2 = 5(3 + x)
-2x + 2x2 = (3 * 5 + x * 5)
-2x + 2x2 = (15 + 5x)

Solving
-2x + 2x2 = 15 + 5x

Solving for variable 'x'.

Reorder the terms:
-15 + -2x + -5x + 2x2 = 15 + 5x + -15 + -5x

Combine like terms: -2x + -5x = -7x
-15 + -7x + 2x2 = 15 + 5x + -15 + -5x

Reorder the terms:
-15 + -7x + 2x2 = 15 + -15 + 5x + -5x

Combine like terms: 15 + -15 = 0
-15 + -7x + 2x2 = 0 + 5x + -5x
-15 + -7x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 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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