(2x+3)(x-5)=-18

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Solution for (2x+3)(x-5)=-18 equation: 


Simplifying
(2x + 3)(x + -5) = -18

Reorder the terms:
(3 + 2x)(x + -5) = -18

Reorder the terms:
(3 + 2x)(-5 + x) = -18

Multiply (3 + 2x) * (-5 + x)
(3(-5 + x) + 2x * (-5 + x)) = -18
((-5 * 3 + x * 3) + 2x * (-5 + x)) = -18
((-15 + 3x) + 2x * (-5 + x)) = -18
(-15 + 3x + (-5 * 2x + x * 2x)) = -18
(-15 + 3x + (-10x + 2x2)) = -18

Combine like terms: 3x + -10x = -7x
(-15 + -7x + 2x2) = -18

Solving
-15 + -7x + 2x2 = -18

Solving for variable 'x'.

Reorder the terms:
-15 + 18 + -7x + 2x2 = -18 + 18

Combine like terms: -15 + 18 = 3
3 + -7x + 2x2 = -18 + 18

Combine like terms: -18 + 18 = 0
3 + -7x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}

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