x^2+(3x-9)*(3x-9)=25

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Solution for x^2+(3x-9)*(3x-9)=25 equation: 


Simplifying
x2 + (3x + -9)(3x + -9) = 25

Reorder the terms:
x2 + (-9 + 3x)(3x + -9) = 25

Reorder the terms:
x2 + (-9 + 3x)(-9 + 3x) = 25

Multiply (-9 + 3x) * (-9 + 3x)
x2 + (-9(-9 + 3x) + 3x * (-9 + 3x)) = 25
x2 + ((-9 * -9 + 3x * -9) + 3x * (-9 + 3x)) = 25
x2 + ((81 + -27x) + 3x * (-9 + 3x)) = 25
x2 + (81 + -27x + (-9 * 3x + 3x * 3x)) = 25
x2 + (81 + -27x + (-27x + 9x2)) = 25

Combine like terms: -27x + -27x = -54x
x2 + (81 + -54x + 9x2) = 25

Reorder the terms:
81 + -54x + x2 + 9x2 = 25

Combine like terms: x2 + 9x2 = 10x2
81 + -54x + 10x2 = 25

Solving
81 + -54x + 10x2 = 25

Solving for variable 'x'.

Reorder the terms:
81 + -25 + -54x + 10x2 = 25 + -25

Combine like terms: 81 + -25 = 56
56 + -54x + 10x2 = 25 + -25

Combine like terms: 25 + -25 = 0
56 + -54x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -27x + 5x2) = 0

Factor a trinomial.
2((7 + -5x)(4 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {1.4, 4}

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