-7-6x-9+7x-7x+90x=7x(3x)

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Solution for -7-6x-9+7x-7x+90x=7x(3x) equation:


Simplifying
-7 + -6x + -9 + 7x + -7x + 90x = 7x(3x)

Reorder the terms:
-7 + -9 + -6x + 7x + -7x + 90x = 7x(3x)

Combine like terms: -7 + -9 = -16
-16 + -6x + 7x + -7x + 90x = 7x(3x)

Combine like terms: -6x + 7x = 1x
-16 + 1x + -7x + 90x = 7x(3x)

Combine like terms: 1x + -7x = -6x
-16 + -6x + 90x = 7x(3x)

Combine like terms: -6x + 90x = 84x
-16 + 84x = 7x(3x)

Remove parenthesis around (3x)
-16 + 84x = 7x * 3x

Reorder the terms for easier multiplication:
-16 + 84x = 7 * 3x * x

Multiply 7 * 3
-16 + 84x = 21x * x

Multiply x * x
-16 + 84x = 21x2

Solving
-16 + 84x = 21x2

Solving for variable 'x'.

Combine like terms: 21x2 + -21x2 = 0
-16 + 84x + -21x2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
0.7619047619 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.7619047619' to each side of the equation.
0.7619047619 + -4x + -0.7619047619 + x2 = 0 + -0.7619047619

Reorder the terms:
0.7619047619 + -0.7619047619 + -4x + x2 = 0 + -0.7619047619

Combine like terms: 0.7619047619 + -0.7619047619 = 0.0000000000
0.0000000000 + -4x + x2 = 0 + -0.7619047619
-4x + x2 = 0 + -0.7619047619

Combine like terms: 0 + -0.7619047619 = -0.7619047619
-4x + x2 = -0.7619047619

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -0.7619047619 + 4

Reorder the terms:
4 + -4x + x2 = -0.7619047619 + 4

Combine like terms: -0.7619047619 + 4 = 3.2380952381
4 + -4x + x2 = 3.2380952381

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.2380952381

Calculate the square root of the right side: 1.799470822

Break this problem into two subproblems by setting 
(x + -2) equal to 1.799470822 and -1.799470822.

Subproblem 1

x + -2 = 1.799470822 Simplifying x + -2 = 1.799470822 Reorder the terms: -2 + x = 1.799470822 Solving -2 + x = 1.799470822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.799470822 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.799470822 + 2 x = 1.799470822 + 2 Combine like terms: 1.799470822 + 2 = 3.799470822 x = 3.799470822 Simplifying x = 3.799470822

Subproblem 2

x + -2 = -1.799470822 Simplifying x + -2 = -1.799470822 Reorder the terms: -2 + x = -1.799470822 Solving -2 + x = -1.799470822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.799470822 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.799470822 + 2 x = -1.799470822 + 2 Combine like terms: -1.799470822 + 2 = 0.200529178 x = 0.200529178 Simplifying x = 0.200529178

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.799470822, 0.200529178}

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