(x+2)(2x-5)=180

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Solution for (x+2)(2x-5)=180 equation: 


Simplifying
(x + 2)(2x + -5) = 180

Reorder the terms:
(2 + x)(2x + -5) = 180

Reorder the terms:
(2 + x)(-5 + 2x) = 180

Multiply (2 + x) * (-5 + 2x)
(2(-5 + 2x) + x(-5 + 2x)) = 180
((-5 * 2 + 2x * 2) + x(-5 + 2x)) = 180
((-10 + 4x) + x(-5 + 2x)) = 180
(-10 + 4x + (-5 * x + 2x * x)) = 180
(-10 + 4x + (-5x + 2x2)) = 180

Combine like terms: 4x + -5x = -1x
(-10 + -1x + 2x2) = 180

Solving
-10 + -1x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-10 + -180 + -1x + 2x2 = 180 + -180

Combine like terms: -10 + -180 = -190
-190 + -1x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-190 + -1x + 2x2 = 0

Factor a trinomial.
(-19 + -2x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-9.5, 10}

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