(14+2x)(24+2x)=600

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Solution for (14+2x)(24+2x)=600 equation: 


Simplifying
(14 + 2x)(24 + 2x) = 600

Multiply (14 + 2x) * (24 + 2x)
(14(24 + 2x) + 2x * (24 + 2x)) = 600
((24 * 14 + 2x * 14) + 2x * (24 + 2x)) = 600
((336 + 28x) + 2x * (24 + 2x)) = 600
(336 + 28x + (24 * 2x + 2x * 2x)) = 600
(336 + 28x + (48x + 4x2)) = 600

Combine like terms: 28x + 48x = 76x
(336 + 76x + 4x2) = 600

Solving
336 + 76x + 4x2 = 600

Solving for variable 'x'.

Reorder the terms:
336 + -600 + 76x + 4x2 = 600 + -600

Combine like terms: 336 + -600 = -264
-264 + 76x + 4x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-264 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-66 + 19x + x2) = 0

Factor a trinomial.
4((-22 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-22, 3}

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