(2x+20)(2x+15)=1400

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Solution for (2x+20)(2x+15)=1400 equation: 


Simplifying
(2x + 20)(2x + 15) = 1400

Reorder the terms:
(20 + 2x)(2x + 15) = 1400

Reorder the terms:
(20 + 2x)(15 + 2x) = 1400

Multiply (20 + 2x) * (15 + 2x)
(20(15 + 2x) + 2x * (15 + 2x)) = 1400
((15 * 20 + 2x * 20) + 2x * (15 + 2x)) = 1400
((300 + 40x) + 2x * (15 + 2x)) = 1400
(300 + 40x + (15 * 2x + 2x * 2x)) = 1400
(300 + 40x + (30x + 4x2)) = 1400

Combine like terms: 40x + 30x = 70x
(300 + 70x + 4x2) = 1400

Solving
300 + 70x + 4x2 = 1400

Solving for variable 'x'.

Reorder the terms:
300 + -1400 + 70x + 4x2 = 1400 + -1400

Combine like terms: 300 + -1400 = -1100
-1100 + 70x + 4x2 = 1400 + -1400

Combine like terms: 1400 + -1400 = 0
-1100 + 70x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-550 + 35x + 2x2) = 0

Factor a trinomial.
2((-55 + -2x)(10 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-55 + -2x)' equal to zero and attempt to solve:

Simplifying
-55 + -2x = 0

Solving
-55 + -2x = 0

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

Add '55' to each side of the equation.
-55 + 55 + -2x = 0 + 55

Combine like terms: -55 + 55 = 0
0 + -2x = 0 + 55
-2x = 0 + 55

Combine like terms: 0 + 55 = 55
-2x = 55

Divide each side by '-2'.
x = -27.5

Simplifying
x = -27.5

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 = {-27.5, 10}

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