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

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


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

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

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

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

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

Reorder the terms:
-2 + -3x + 2x2 = 2(5 + x)
-2 + -3x + 2x2 = (5 * 2 + x * 2)
-2 + -3x + 2x2 = (10 + 2x)

Solving
-2 + -3x + 2x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-2 + -10 + -3x + -2x + 2x2 = 10 + 2x + -10 + -2x

Combine like terms: -2 + -10 = -12
-12 + -3x + -2x + 2x2 = 10 + 2x + -10 + -2x

Combine like terms: -3x + -2x = -5x
-12 + -5x + 2x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-12 + -5x + 2x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-12 + -5x + 2x2 = 0 + 2x + -2x
-12 + -5x + 2x2 = 2x + -2x

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

Factor a trinomial.
(-3 + -2x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}

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