(45+2X)(35+2X)=3575

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Solution for (45+2X)(35+2X)=3575 equation: 


Simplifying
(45 + 2X)(35 + 2X) = 3575

Multiply (45 + 2X) * (35 + 2X)
(45(35 + 2X) + 2X * (35 + 2X)) = 3575
((35 * 45 + 2X * 45) + 2X * (35 + 2X)) = 3575
((1575 + 90X) + 2X * (35 + 2X)) = 3575
(1575 + 90X + (35 * 2X + 2X * 2X)) = 3575
(1575 + 90X + (70X + 4X2)) = 3575

Combine like terms: 90X + 70X = 160X
(1575 + 160X + 4X2) = 3575

Solving
1575 + 160X + 4X2 = 3575

Solving for variable 'X'.

Reorder the terms:
1575 + -3575 + 160X + 4X2 = 3575 + -3575

Combine like terms: 1575 + -3575 = -2000
-2000 + 160X + 4X2 = 3575 + -3575

Combine like terms: 3575 + -3575 = 0
-2000 + 160X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-500 + 40X + X2) = 0

Factor a trinomial.
4((-50 + -1X)(10 + -1X)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-50 + -1X)' equal to zero and attempt to solve:

Simplifying
-50 + -1X = 0

Solving
-50 + -1X = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1X = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1X = 0 + 50
-1X = 0 + 50

Combine like terms: 0 + 50 = 50
-1X = 50

Divide each side by '-1'.
X = -50

Simplifying
X = -50

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 = {-50, 10}

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