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

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


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

Reorder the terms:
2x(3 + x) + -5 = -3(x + -2)
(3 * 2x + x * 2x) + -5 = -3(x + -2)
(6x + 2x2) + -5 = -3(x + -2)

Reorder the terms:
-5 + 6x + 2x2 = -3(x + -2)

Reorder the terms:
-5 + 6x + 2x2 = -3(-2 + x)
-5 + 6x + 2x2 = (-2 * -3 + x * -3)
-5 + 6x + 2x2 = (6 + -3x)

Solving
-5 + 6x + 2x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
-5 + -6 + 6x + 3x + 2x2 = 6 + -3x + -6 + 3x

Combine like terms: -5 + -6 = -11
-11 + 6x + 3x + 2x2 = 6 + -3x + -6 + 3x

Combine like terms: 6x + 3x = 9x
-11 + 9x + 2x2 = 6 + -3x + -6 + 3x

Reorder the terms:
-11 + 9x + 2x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
-11 + 9x + 2x2 = 0 + -3x + 3x
-11 + 9x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-11 + 9x + 2x2 = 0

Factor a trinomial.
(-11 + -2x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -2x)' equal to zero and attempt to solve:

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5

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

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-5.5, 1}

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