(2x-23)(2x+5)=60

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Solution for (2x-23)(2x+5)=60 equation: 


Simplifying
(2x + -23)(2x + 5) = 60

Reorder the terms:
(-23 + 2x)(2x + 5) = 60

Reorder the terms:
(-23 + 2x)(5 + 2x) = 60

Multiply (-23 + 2x) * (5 + 2x)
(-23(5 + 2x) + 2x * (5 + 2x)) = 60
((5 * -23 + 2x * -23) + 2x * (5 + 2x)) = 60
((-115 + -46x) + 2x * (5 + 2x)) = 60
(-115 + -46x + (5 * 2x + 2x * 2x)) = 60
(-115 + -46x + (10x + 4x2)) = 60

Combine like terms: -46x + 10x = -36x
(-115 + -36x + 4x2) = 60

Solving
-115 + -36x + 4x2 = 60

Solving for variable 'x'.

Reorder the terms:
-115 + -60 + -36x + 4x2 = 60 + -60

Combine like terms: -115 + -60 = -175
-175 + -36x + 4x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-175 + -36x + 4x2 = 0

Factor a trinomial.
(-7 + -2x)(25 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(25 + -2x)' equal to zero and attempt to solve:

Simplifying
25 + -2x = 0

Solving
25 + -2x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -2x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -2x = 0 + -25
-2x = 0 + -25

Combine like terms: 0 + -25 = -25
-2x = -25

Divide each side by '-2'.
x = 12.5

Simplifying
x = 12.5
Solution
x = {-3.5, 12.5}

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