(2x+15)(2x+20)=414

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Solution for (2x+15)(2x+20)=414 equation: 


Simplifying
(2x + 15)(2x + 20) = 414

Reorder the terms:
(15 + 2x)(2x + 20) = 414

Reorder the terms:
(15 + 2x)(20 + 2x) = 414

Multiply (15 + 2x) * (20 + 2x)
(15(20 + 2x) + 2x * (20 + 2x)) = 414
((20 * 15 + 2x * 15) + 2x * (20 + 2x)) = 414
((300 + 30x) + 2x * (20 + 2x)) = 414
(300 + 30x + (20 * 2x + 2x * 2x)) = 414
(300 + 30x + (40x + 4x2)) = 414

Combine like terms: 30x + 40x = 70x
(300 + 70x + 4x2) = 414

Solving
300 + 70x + 4x2 = 414

Solving for variable 'x'.

Reorder the terms:
300 + -414 + 70x + 4x2 = 414 + -414

Combine like terms: 300 + -414 = -114
-114 + 70x + 4x2 = 414 + -414

Combine like terms: 414 + -414 = 0
-114 + 70x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-57 + 35x + 2x2) = 0

Factor a trinomial.
2((-19 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

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

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 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 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19

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 = {-19, 1.5}

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