(4x-10)(3x+7)=180

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Solution for (4x-10)(3x+7)=180 equation: 


Simplifying
(4x + -10)(3x + 7) = 180

Reorder the terms:
(-10 + 4x)(3x + 7) = 180

Reorder the terms:
(-10 + 4x)(7 + 3x) = 180

Multiply (-10 + 4x) * (7 + 3x)
(-10(7 + 3x) + 4x * (7 + 3x)) = 180
((7 * -10 + 3x * -10) + 4x * (7 + 3x)) = 180
((-70 + -30x) + 4x * (7 + 3x)) = 180
(-70 + -30x + (7 * 4x + 3x * 4x)) = 180
(-70 + -30x + (28x + 12x2)) = 180

Combine like terms: -30x + 28x = -2x
(-70 + -2x + 12x2) = 180

Solving
-70 + -2x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
-70 + -180 + -2x + 12x2 = 180 + -180

Combine like terms: -70 + -180 = -250
-250 + -2x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-250 + -2x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + -1x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + -1x + 6x2)' equal to zero and attempt to solve:

Simplifying
-125 + -1x + 6x2 = 0

Solving
-125 + -1x + 6x2 = 0

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

Divide each side by '6'.
-20.83333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '20.83333333' to each side of the equation.
-20.83333333 + -0.1666666667x + 20.83333333 + x2 = 0 + 20.83333333

Reorder the terms:
-20.83333333 + 20.83333333 + -0.1666666667x + x2 = 0 + 20.83333333

Combine like terms: -20.83333333 + 20.83333333 = 0.00000000
0.00000000 + -0.1666666667x + x2 = 0 + 20.83333333
-0.1666666667x + x2 = 0 + 20.83333333

Combine like terms: 0 + 20.83333333 = 20.83333333
-0.1666666667x + x2 = 20.83333333

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 20.83333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 20.83333333 + 0.006944444447

Combine like terms: 20.83333333 + 0.006944444447 = 20.840277774447
0.006944444447 + -0.1666666667x + x2 = 20.840277774447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 20.840277774447

Calculate the square root of the right side: 4.565115308

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 4.565115308 and -4.565115308.


Subproblem 1
x + -0.08333333335 = 4.565115308

Simplifying
x + -0.08333333335 = 4.565115308

Reorder the terms:
-0.08333333335 + x = 4.565115308

Solving
-0.08333333335 + x = 4.565115308

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 4.565115308 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 4.565115308 + 0.08333333335
x = 4.565115308 + 0.08333333335

Combine like terms: 4.565115308 + 0.08333333335 = 4.64844864135
x = 4.64844864135

Simplifying
x = 4.64844864135


Subproblem 2
x + -0.08333333335 = -4.565115308

Simplifying
x + -0.08333333335 = -4.565115308

Reorder the terms:
-0.08333333335 + x = -4.565115308

Solving
-0.08333333335 + x = -4.565115308

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -4.565115308 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -4.565115308 + 0.08333333335
x = -4.565115308 + 0.08333333335

Combine like terms: -4.565115308 + 0.08333333335 = -4.48178197465
x = -4.48178197465

Simplifying
x = -4.48178197465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.64844864135, -4.48178197465}
Solution
x = {4.64844864135, -4.48178197465}

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