(x+27)(x+27)=(2x-10)(2x-10)

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Solution for (x+27)(x+27)=(2x-10)(2x-10) equation: 


Simplifying
(x + 27)(x + 27) = (2x + -10)(2x + -10)

Reorder the terms:
(27 + x)(x + 27) = (2x + -10)(2x + -10)

Reorder the terms:
(27 + x)(27 + x) = (2x + -10)(2x + -10)

Multiply (27 + x) * (27 + x)
(27(27 + x) + x(27 + x)) = (2x + -10)(2x + -10)
((27 * 27 + x * 27) + x(27 + x)) = (2x + -10)(2x + -10)
((729 + 27x) + x(27 + x)) = (2x + -10)(2x + -10)
(729 + 27x + (27 * x + x * x)) = (2x + -10)(2x + -10)
(729 + 27x + (27x + x2)) = (2x + -10)(2x + -10)

Combine like terms: 27x + 27x = 54x
(729 + 54x + x2) = (2x + -10)(2x + -10)

Reorder the terms:
729 + 54x + x2 = (-10 + 2x)(2x + -10)

Reorder the terms:
729 + 54x + x2 = (-10 + 2x)(-10 + 2x)

Multiply (-10 + 2x) * (-10 + 2x)
729 + 54x + x2 = (-10(-10 + 2x) + 2x * (-10 + 2x))
729 + 54x + x2 = ((-10 * -10 + 2x * -10) + 2x * (-10 + 2x))
729 + 54x + x2 = ((100 + -20x) + 2x * (-10 + 2x))
729 + 54x + x2 = (100 + -20x + (-10 * 2x + 2x * 2x))
729 + 54x + x2 = (100 + -20x + (-20x + 4x2))

Combine like terms: -20x + -20x = -40x
729 + 54x + x2 = (100 + -40x + 4x2)

Solving
729 + 54x + x2 = 100 + -40x + 4x2

Solving for variable 'x'.

Reorder the terms:
729 + -100 + 54x + 40x + x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 729 + -100 = 629
629 + 54x + 40x + x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 54x + 40x = 94x
629 + 94x + x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: x2 + -4x2 = -3x2
629 + 94x + -3x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Reorder the terms:
629 + 94x + -3x2 = 100 + -100 + -40x + 40x + 4x2 + -4x2

Combine like terms: 100 + -100 = 0
629 + 94x + -3x2 = 0 + -40x + 40x + 4x2 + -4x2
629 + 94x + -3x2 = -40x + 40x + 4x2 + -4x2

Combine like terms: -40x + 40x = 0
629 + 94x + -3x2 = 0 + 4x2 + -4x2
629 + 94x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
629 + 94x + -3x2 = 0

Factor a trinomial.
(37 + -1x)(17 + 3x) = 0


Subproblem 1
Set the factor '(37 + -1x)' equal to zero and attempt to solve:

Simplifying
37 + -1x = 0

Solving
37 + -1x = 0

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

Add '-37' to each side of the equation.
37 + -37 + -1x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -1x = 0 + -37
-1x = 0 + -37

Combine like terms: 0 + -37 = -37
-1x = -37

Divide each side by '-1'.
x = 37

Simplifying
x = 37

Subproblem 2
Set the factor '(17 + 3x)' equal to zero and attempt to solve:

Simplifying
17 + 3x = 0

Solving
17 + 3x = 0

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

Add '-17' to each side of the equation.
17 + -17 + 3x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 3x = 0 + -17
3x = 0 + -17

Combine like terms: 0 + -17 = -17
3x = -17

Divide each side by '3'.
x = -5.666666667

Simplifying
x = -5.666666667
Solution
x = {37, -5.666666667}

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