(2x+1)(x-2)=18

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Solution for (2x+1)(x-2)=18 equation: 


Simplifying
(2x + 1)(x + -2) = 18

Reorder the terms:
(1 + 2x)(x + -2) = 18

Reorder the terms:
(1 + 2x)(-2 + x) = 18

Multiply (1 + 2x) * (-2 + x)
(1(-2 + x) + 2x * (-2 + x)) = 18
((-2 * 1 + x * 1) + 2x * (-2 + x)) = 18
((-2 + 1x) + 2x * (-2 + x)) = 18
(-2 + 1x + (-2 * 2x + x * 2x)) = 18
(-2 + 1x + (-4x + 2x2)) = 18

Combine like terms: 1x + -4x = -3x
(-2 + -3x + 2x2) = 18

Solving
-2 + -3x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
-2 + -18 + -3x + 2x2 = 18 + -18

Combine like terms: -2 + -18 = -20
-20 + -3x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-20 + -3x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

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

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

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 4}

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