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

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


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

Reorder the terms:
7x(-3 + x) = 4(x + 5)
(-3 * 7x + x * 7x) = 4(x + 5)
(-21x + 7x2) = 4(x + 5)

Reorder the terms:
-21x + 7x2 = 4(5 + x)
-21x + 7x2 = (5 * 4 + x * 4)
-21x + 7x2 = (20 + 4x)

Solving
-21x + 7x2 = 20 + 4x

Solving for variable 'x'.

Reorder the terms:
-20 + -21x + -4x + 7x2 = 20 + 4x + -20 + -4x

Combine like terms: -21x + -4x = -25x
-20 + -25x + 7x2 = 20 + 4x + -20 + -4x

Reorder the terms:
-20 + -25x + 7x2 = 20 + -20 + 4x + -4x

Combine like terms: 20 + -20 = 0
-20 + -25x + 7x2 = 0 + 4x + -4x
-20 + -25x + 7x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-20 + -25x + 7x2 = 0

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

Divide each side by '7'.
-2.857142857 + -3.571428571x + x2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + -3.571428571x + 2.857142857 + x2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + -3.571428571x + x2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + -3.571428571x + x2 = 0 + 2.857142857
-3.571428571x + x2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
-3.571428571x + x2 = 2.857142857

The x term is -3.571428571x.  Take half its coefficient (-1.785714286).
Square it (3.188775511) and add it to both sides.

Add '3.188775511' to each side of the equation.
-3.571428571x + 3.188775511 + x2 = 2.857142857 + 3.188775511

Reorder the terms:
3.188775511 + -3.571428571x + x2 = 2.857142857 + 3.188775511

Combine like terms: 2.857142857 + 3.188775511 = 6.045918368
3.188775511 + -3.571428571x + x2 = 6.045918368

Factor a perfect square on the left side:
(x + -1.785714286)(x + -1.785714286) = 6.045918368

Calculate the square root of the right side: 2.458844926

Break this problem into two subproblems by setting 
(x + -1.785714286) equal to 2.458844926 and -2.458844926.

Subproblem 1

x + -1.785714286 = 2.458844926 Simplifying x + -1.785714286 = 2.458844926 Reorder the terms: -1.785714286 + x = 2.458844926 Solving -1.785714286 + x = 2.458844926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 2.458844926 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 2.458844926 + 1.785714286 x = 2.458844926 + 1.785714286 Combine like terms: 2.458844926 + 1.785714286 = 4.244559212 x = 4.244559212 Simplifying x = 4.244559212

Subproblem 2

x + -1.785714286 = -2.458844926 Simplifying x + -1.785714286 = -2.458844926 Reorder the terms: -1.785714286 + x = -2.458844926 Solving -1.785714286 + x = -2.458844926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -2.458844926 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -2.458844926 + 1.785714286 x = -2.458844926 + 1.785714286 Combine like terms: -2.458844926 + 1.785714286 = -0.67313064 x = -0.67313064 Simplifying x = -0.67313064

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.244559212, -0.67313064}

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