(2x+5)(2x+7)-35=45

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Solution for (2x+5)(2x+7)-35=45 equation: 


Simplifying
(2x + 5)(2x + 7) + -35 = 45

Reorder the terms:
(5 + 2x)(2x + 7) + -35 = 45

Reorder the terms:
(5 + 2x)(7 + 2x) + -35 = 45

Multiply (5 + 2x) * (7 + 2x)
(5(7 + 2x) + 2x * (7 + 2x)) + -35 = 45
((7 * 5 + 2x * 5) + 2x * (7 + 2x)) + -35 = 45
((35 + 10x) + 2x * (7 + 2x)) + -35 = 45
(35 + 10x + (7 * 2x + 2x * 2x)) + -35 = 45
(35 + 10x + (14x + 4x2)) + -35 = 45

Combine like terms: 10x + 14x = 24x
(35 + 24x + 4x2) + -35 = 45

Reorder the terms:
35 + -35 + 24x + 4x2 = 45

Combine like terms: 35 + -35 = 0
0 + 24x + 4x2 = 45
24x + 4x2 = 45

Solving
24x + 4x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + 24x + 4x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 24x + 4x2 = 0

Factor a trinomial.
(-15 + -2x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-7.5, 1.5}

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