(2x+3)(x-5)=7

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Solution for (2x+3)(x-5)=7 equation: 


Simplifying
(2x + 3)(x + -5) = 7

Reorder the terms:
(3 + 2x)(x + -5) = 7

Reorder the terms:
(3 + 2x)(-5 + x) = 7

Multiply (3 + 2x) * (-5 + x)
(3(-5 + x) + 2x * (-5 + x)) = 7
((-5 * 3 + x * 3) + 2x * (-5 + x)) = 7
((-15 + 3x) + 2x * (-5 + x)) = 7
(-15 + 3x + (-5 * 2x + x * 2x)) = 7
(-15 + 3x + (-10x + 2x2)) = 7

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

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

Solving for variable 'x'.

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

Combine like terms: -15 + -7 = -22
-22 + -7x + 2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-22 + -7x + 2x2 = 0

Factor a trinomial.
(-2 + -1x)(11 + -2x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-2, 5.5}

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