3x(2x-5)-2(4x-7)=

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Solution for 3x(2x-5)-2(4x-7)= equation: 


Simplifying
3x(2x + -5) + -2(4x + -7) = 0

Reorder the terms:
3x(-5 + 2x) + -2(4x + -7) = 0
(-5 * 3x + 2x * 3x) + -2(4x + -7) = 0
(-15x + 6x2) + -2(4x + -7) = 0

Reorder the terms:
-15x + 6x2 + -2(-7 + 4x) = 0
-15x + 6x2 + (-7 * -2 + 4x * -2) = 0
-15x + 6x2 + (14 + -8x) = 0

Reorder the terms:
14 + -15x + -8x + 6x2 = 0

Combine like terms: -15x + -8x = -23x
14 + -23x + 6x2 = 0

Solving
14 + -23x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
2.333333333 + -3.833333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -3.833333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -3.833333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -3.833333333x + x2 = 0 + -2.333333333
-3.833333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-3.833333333x + x2 = -2.333333333

The x term is -3.833333333x.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333x + 3.673611112 + x2 = -2.333333333 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333x + x2 = -2.333333333 + 3.673611112

Combine like terms: -2.333333333 + 3.673611112 = 1.340277779
3.673611112 + -3.833333333x + x2 = 1.340277779

Factor a perfect square on the left side:
(x + -1.916666667)(x + -1.916666667) = 1.340277779

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(x + -1.916666667) equal to 1.157703666 and -1.157703666.


Subproblem 1
x + -1.916666667 = 1.157703666

Simplifying
x + -1.916666667 = 1.157703666

Reorder the terms:
-1.916666667 + x = 1.157703666

Solving
-1.916666667 + x = 1.157703666

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = 1.157703666 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = 1.157703666 + 1.916666667
x = 1.157703666 + 1.916666667

Combine like terms: 1.157703666 + 1.916666667 = 3.074370333
x = 3.074370333

Simplifying
x = 3.074370333


Subproblem 2
x + -1.916666667 = -1.157703666

Simplifying
x + -1.916666667 = -1.157703666

Reorder the terms:
-1.916666667 + x = -1.157703666

Solving
-1.916666667 + x = -1.157703666

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = -1.157703666 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = -1.157703666 + 1.916666667
x = -1.157703666 + 1.916666667

Combine like terms: -1.157703666 + 1.916666667 = 0.758963001
x = 0.758963001

Simplifying
x = 0.758963001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.074370333, 0.758963001}

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