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

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


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

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

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

Multiply (-1 + 2x) * (5 + 3x)
(-1(5 + 3x) + 2x * (5 + 3x)) = (x + 2)(2x + -1)
((5 * -1 + 3x * -1) + 2x * (5 + 3x)) = (x + 2)(2x + -1)
((-5 + -3x) + 2x * (5 + 3x)) = (x + 2)(2x + -1)
(-5 + -3x + (5 * 2x + 3x * 2x)) = (x + 2)(2x + -1)
(-5 + -3x + (10x + 6x2)) = (x + 2)(2x + -1)

Combine like terms: -3x + 10x = 7x
(-5 + 7x + 6x2) = (x + 2)(2x + -1)

Reorder the terms:
-5 + 7x + 6x2 = (2 + x)(2x + -1)

Reorder the terms:
-5 + 7x + 6x2 = (2 + x)(-1 + 2x)

Multiply (2 + x) * (-1 + 2x)
-5 + 7x + 6x2 = (2(-1 + 2x) + x(-1 + 2x))
-5 + 7x + 6x2 = ((-1 * 2 + 2x * 2) + x(-1 + 2x))
-5 + 7x + 6x2 = ((-2 + 4x) + x(-1 + 2x))
-5 + 7x + 6x2 = (-2 + 4x + (-1 * x + 2x * x))
-5 + 7x + 6x2 = (-2 + 4x + (-1x + 2x2))

Combine like terms: 4x + -1x = 3x
-5 + 7x + 6x2 = (-2 + 3x + 2x2)

Solving
-5 + 7x + 6x2 = -2 + 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 2 + 7x + -3x + 6x2 + -2x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2

Combine like terms: -5 + 2 = -3
-3 + 7x + -3x + 6x2 + -2x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2

Combine like terms: 7x + -3x = 4x
-3 + 4x + 6x2 + -2x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-3 + 4x + 4x2 = -2 + 3x + 2x2 + 2 + -3x + -2x2

Reorder the terms:
-3 + 4x + 4x2 = -2 + 2 + 3x + -3x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
-3 + 4x + 4x2 = 0 + 3x + -3x + 2x2 + -2x2
-3 + 4x + 4x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
-3 + 4x + 4x2 = 0 + 2x2 + -2x2
-3 + 4x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 4x + 4x2 = 0

Factor a trinomial.
(-3 + -2x)(1 + -2x) = 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 '(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
Solution
x = {-1.5, 0.5}

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