144=(20-2x)(10-2x)

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Solution for 144=(20-2x)(10-2x) equation: 


Simplifying
144 = (20 + -2x)(10 + -2x)

Multiply (20 + -2x) * (10 + -2x)
144 = (20(10 + -2x) + -2x * (10 + -2x))
144 = ((10 * 20 + -2x * 20) + -2x * (10 + -2x))
144 = ((200 + -40x) + -2x * (10 + -2x))
144 = (200 + -40x + (10 * -2x + -2x * -2x))
144 = (200 + -40x + (-20x + 4x2))

Combine like terms: -40x + -20x = -60x
144 = (200 + -60x + 4x2)

Solving
144 = 200 + -60x + 4x2

Solving for variable 'x'.

Combine like terms: 144 + -200 = -56
-56 + 60x + -4x2 = 200 + -60x + 4x2 + -200 + 60x + -4x2

Reorder the terms:
-56 + 60x + -4x2 = 200 + -200 + -60x + 60x + 4x2 + -4x2

Combine like terms: 200 + -200 = 0
-56 + 60x + -4x2 = 0 + -60x + 60x + 4x2 + -4x2
-56 + 60x + -4x2 = -60x + 60x + 4x2 + -4x2

Combine like terms: -60x + 60x = 0
-56 + 60x + -4x2 = 0 + 4x2 + -4x2
-56 + 60x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-56 + 60x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 15x + -1x2) = 0

Factor a trinomial.
4((-14 + x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-14 + x)' equal to zero and attempt to solve:

Simplifying
-14 + x = 0

Solving
-14 + x = 0

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

Add '14' to each side of the equation.
-14 + 14 + x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + x = 0 + 14
x = 0 + 14

Combine like terms: 0 + 14 = 14
x = 14

Simplifying
x = 14

Subproblem 2
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
Solution
x = {14, 1}

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