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

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


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

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

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

Multiply (-9 + 3x) * (7 + x)
(-9(7 + x) + 3x * (7 + x)) = 90
((7 * -9 + x * -9) + 3x * (7 + x)) = 90
((-63 + -9x) + 3x * (7 + x)) = 90
(-63 + -9x + (7 * 3x + x * 3x)) = 90
(-63 + -9x + (21x + 3x2)) = 90

Combine like terms: -9x + 21x = 12x
(-63 + 12x + 3x2) = 90

Solving
-63 + 12x + 3x2 = 90

Solving for variable 'x'.

Reorder the terms:
-63 + -90 + 12x + 3x2 = 90 + -90

Combine like terms: -63 + -90 = -153
-153 + 12x + 3x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-153 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-51 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-51 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-51 + 4x + x2 = 0

Solving
-51 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 4x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 4x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 4x + x2 = 0 + 51
4x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
4x + x2 = 51

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 = 51 + 4

Reorder the terms:
4 + 4x + x2 = 51 + 4

Combine like terms: 51 + 4 = 55
4 + 4x + x2 = 55

Factor a perfect square on the left side:
(x + 2)(x + 2) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 2) equal to 7.416198487 and -7.416198487.


Subproblem 1
x + 2 = 7.416198487

Simplifying
x + 2 = 7.416198487

Reorder the terms:
2 + x = 7.416198487

Solving
2 + x = 7.416198487

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 = 7.416198487 + -2

Combine like terms: 2 + -2 = 0
0 + x = 7.416198487 + -2
x = 7.416198487 + -2

Combine like terms: 7.416198487 + -2 = 5.416198487
x = 5.416198487

Simplifying
x = 5.416198487


Subproblem 2
x + 2 = -7.416198487

Simplifying
x + 2 = -7.416198487

Reorder the terms:
2 + x = -7.416198487

Solving
2 + x = -7.416198487

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 = -7.416198487 + -2

Combine like terms: 2 + -2 = 0
0 + x = -7.416198487 + -2
x = -7.416198487 + -2

Combine like terms: -7.416198487 + -2 = -9.416198487
x = -9.416198487

Simplifying
x = -9.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.416198487, -9.416198487}
Solution
x = {5.416198487, -9.416198487}

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