7x(x-2)-27=2x(x-4)

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Solution for 7x(x-2)-27=2x(x-4) equation: 


Simplifying
7x(x + -2) + -27 = 2x(x + -4)

Reorder the terms:
7x(-2 + x) + -27 = 2x(x + -4)
(-2 * 7x + x * 7x) + -27 = 2x(x + -4)
(-14x + 7x2) + -27 = 2x(x + -4)

Reorder the terms:
-27 + -14x + 7x2 = 2x(x + -4)

Reorder the terms:
-27 + -14x + 7x2 = 2x(-4 + x)
-27 + -14x + 7x2 = (-4 * 2x + x * 2x)
-27 + -14x + 7x2 = (-8x + 2x2)

Solving
-27 + -14x + 7x2 = -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-27 + -14x + 8x + 7x2 + -2x2 = -8x + 2x2 + 8x + -2x2

Combine like terms: -14x + 8x = -6x
-27 + -6x + 7x2 + -2x2 = -8x + 2x2 + 8x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
-27 + -6x + 5x2 = -8x + 2x2 + 8x + -2x2

Reorder the terms:
-27 + -6x + 5x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
-27 + -6x + 5x2 = 0 + 2x2 + -2x2
-27 + -6x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-27 + -6x + 5x2 = 0

Factor a trinomial.
(-9 + -5x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -5x)' equal to zero and attempt to solve:

Simplifying
-9 + -5x = 0

Solving
-9 + -5x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5x = 0 + 9
-5x = 0 + 9

Combine like terms: 0 + 9 = 9
-5x = 9

Divide each side by '-5'.
x = -1.8

Simplifying
x = -1.8

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 = {-1.8, 3}

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