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

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


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

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

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

Multiply (3 + x) * (-1 + 2x)
(3(-1 + 2x) + x(-1 + 2x)) = (3 + -1x)(5 + -3x)
((-1 * 3 + 2x * 3) + x(-1 + 2x)) = (3 + -1x)(5 + -3x)
((-3 + 6x) + x(-1 + 2x)) = (3 + -1x)(5 + -3x)
(-3 + 6x + (-1 * x + 2x * x)) = (3 + -1x)(5 + -3x)
(-3 + 6x + (-1x + 2x2)) = (3 + -1x)(5 + -3x)

Combine like terms: 6x + -1x = 5x
(-3 + 5x + 2x2) = (3 + -1x)(5 + -3x)

Multiply (3 + -1x) * (5 + -3x)
-3 + 5x + 2x2 = (3(5 + -3x) + -1x * (5 + -3x))
-3 + 5x + 2x2 = ((5 * 3 + -3x * 3) + -1x * (5 + -3x))
-3 + 5x + 2x2 = ((15 + -9x) + -1x * (5 + -3x))
-3 + 5x + 2x2 = (15 + -9x + (5 * -1x + -3x * -1x))
-3 + 5x + 2x2 = (15 + -9x + (-5x + 3x2))

Combine like terms: -9x + -5x = -14x
-3 + 5x + 2x2 = (15 + -14x + 3x2)

Solving
-3 + 5x + 2x2 = 15 + -14x + 3x2

Solving for variable 'x'.

Reorder the terms:
-3 + -15 + 5x + 14x + 2x2 + -3x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Combine like terms: -3 + -15 = -18
-18 + 5x + 14x + 2x2 + -3x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Combine like terms: 5x + 14x = 19x
-18 + 19x + 2x2 + -3x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-18 + 19x + -1x2 = 15 + -14x + 3x2 + -15 + 14x + -3x2

Reorder the terms:
-18 + 19x + -1x2 = 15 + -15 + -14x + 14x + 3x2 + -3x2

Combine like terms: 15 + -15 = 0
-18 + 19x + -1x2 = 0 + -14x + 14x + 3x2 + -3x2
-18 + 19x + -1x2 = -14x + 14x + 3x2 + -3x2

Combine like terms: -14x + 14x = 0
-18 + 19x + -1x2 = 0 + 3x2 + -3x2
-18 + 19x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-18 + 19x + -1x2 = 0

Factor a trinomial.
(-18 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-18 + x)' equal to zero and attempt to solve:

Simplifying
-18 + x = 0

Solving
-18 + x = 0

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

Add '18' to each side of the equation.
-18 + 18 + x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + x = 0 + 18
x = 0 + 18

Combine like terms: 0 + 18 = 18
x = 18

Simplifying
x = 18

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 = {18, 1}

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