(14+2x)(26+2x)=589

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Solution for (14+2x)(26+2x)=589 equation: 


Simplifying
(14 + 2x)(26 + 2x) = 589

Multiply (14 + 2x) * (26 + 2x)
(14(26 + 2x) + 2x * (26 + 2x)) = 589
((26 * 14 + 2x * 14) + 2x * (26 + 2x)) = 589
((364 + 28x) + 2x * (26 + 2x)) = 589
(364 + 28x + (26 * 2x + 2x * 2x)) = 589
(364 + 28x + (52x + 4x2)) = 589

Combine like terms: 28x + 52x = 80x
(364 + 80x + 4x2) = 589

Solving
364 + 80x + 4x2 = 589

Solving for variable 'x'.

Reorder the terms:
364 + -589 + 80x + 4x2 = 589 + -589

Combine like terms: 364 + -589 = -225
-225 + 80x + 4x2 = 589 + -589

Combine like terms: 589 + -589 = 0
-225 + 80x + 4x2 = 0

Factor a trinomial.
(-45 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-45 + -2x)' equal to zero and attempt to solve:

Simplifying
-45 + -2x = 0

Solving
-45 + -2x = 0

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

Add '45' to each side of the equation.
-45 + 45 + -2x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -2x = 0 + 45
-2x = 0 + 45

Combine like terms: 0 + 45 = 45
-2x = 45

Divide each side by '-2'.
x = -22.5

Simplifying
x = -22.5

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-22.5, 2.5}

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