(18-2x)(14-2x)=192

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Solution for (18-2x)(14-2x)=192 equation:


Simplifying
(18 + -2x)(14 + -2x) = 192

Multiply (18 + -2x) * (14 + -2x)
(18(14 + -2x) + -2x * (14 + -2x)) = 192
((14 * 18 + -2x * 18) + -2x * (14 + -2x)) = 192
((252 + -36x) + -2x * (14 + -2x)) = 192
(252 + -36x + (14 * -2x + -2x * -2x)) = 192
(252 + -36x + (-28x + 4x2)) = 192

Combine like terms: -36x + -28x = -64x
(252 + -64x + 4x2) = 192

Solving
252 + -64x + 4x2 = 192

Solving for variable 'x'.

Reorder the terms:
252 + -192 + -64x + 4x2 = 192 + -192

Combine like terms: 252 + -192 = 60
60 + -64x + 4x2 = 192 + -192

Combine like terms: 192 + -192 = 0
60 + -64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -16x + x2) = 0

Factor a trinomial.
4((1 + -1x)(15 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {1, 15}

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