3x(4x-7)=15

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Solution for 3x(4x-7)=15 equation: 


Simplifying
3x(4x + -7) = 15

Reorder the terms:
3x(-7 + 4x) = 15
(-7 * 3x + 4x * 3x) = 15
(-21x + 12x2) = 15

Solving
-21x + 12x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -21x + 12x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -21x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -7x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -7x + 4x2)' equal to zero and attempt to solve:

Simplifying
-5 + -7x + 4x2 = 0

Solving
-5 + -7x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.75x + x2 = 0 + 1.25
-1.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.75x + x2 = 1.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1.25 + 0.765625

Combine like terms: 1.25 + 0.765625 = 2.015625
0.765625 + -1.75x + x2 = 2.015625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.419727086 and -1.419727086.


Subproblem 1
x + -0.875 = 1.419727086

Simplifying
x + -0.875 = 1.419727086

Reorder the terms:
-0.875 + x = 1.419727086

Solving
-0.875 + x = 1.419727086

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.419727086 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.419727086 + 0.875
x = 1.419727086 + 0.875

Combine like terms: 1.419727086 + 0.875 = 2.294727086
x = 2.294727086

Simplifying
x = 2.294727086


Subproblem 2
x + -0.875 = -1.419727086

Simplifying
x + -0.875 = -1.419727086

Reorder the terms:
-0.875 + x = -1.419727086

Solving
-0.875 + x = -1.419727086

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.419727086 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.419727086 + 0.875
x = -1.419727086 + 0.875

Combine like terms: -1.419727086 + 0.875 = -0.544727086
x = -0.544727086

Simplifying
x = -0.544727086


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.294727086, -0.544727086}
Solution
x = {2.294727086, -0.544727086}

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