x^2+(10-3x)*(10-3x)=(x+4)*(x+4)

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Solution for x^2+(10-3x)*(10-3x)=(x+4)*(x+4) equation: 


Simplifying
x2 + (10 + -3x)(10 + -3x) = (x + 4)(x + 4)

Multiply (10 + -3x) * (10 + -3x)
x2 + (10(10 + -3x) + -3x * (10 + -3x)) = (x + 4)(x + 4)
x2 + ((10 * 10 + -3x * 10) + -3x * (10 + -3x)) = (x + 4)(x + 4)
x2 + ((100 + -30x) + -3x * (10 + -3x)) = (x + 4)(x + 4)
x2 + (100 + -30x + (10 * -3x + -3x * -3x)) = (x + 4)(x + 4)
x2 + (100 + -30x + (-30x + 9x2)) = (x + 4)(x + 4)

Combine like terms: -30x + -30x = -60x
x2 + (100 + -60x + 9x2) = (x + 4)(x + 4)

Reorder the terms:
100 + -60x + x2 + 9x2 = (x + 4)(x + 4)

Combine like terms: x2 + 9x2 = 10x2
100 + -60x + 10x2 = (x + 4)(x + 4)

Reorder the terms:
100 + -60x + 10x2 = (4 + x)(x + 4)

Reorder the terms:
100 + -60x + 10x2 = (4 + x)(4 + x)

Multiply (4 + x) * (4 + x)
100 + -60x + 10x2 = (4(4 + x) + x(4 + x))
100 + -60x + 10x2 = ((4 * 4 + x * 4) + x(4 + x))
100 + -60x + 10x2 = ((16 + 4x) + x(4 + x))
100 + -60x + 10x2 = (16 + 4x + (4 * x + x * x))
100 + -60x + 10x2 = (16 + 4x + (4x + x2))

Combine like terms: 4x + 4x = 8x
100 + -60x + 10x2 = (16 + 8x + x2)

Solving
100 + -60x + 10x2 = 16 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
100 + -16 + -60x + -8x + 10x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 100 + -16 = 84
84 + -60x + -8x + 10x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: -60x + -8x = -68x
84 + -68x + 10x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 10x2 + -1x2 = 9x2
84 + -68x + 9x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Reorder the terms:
84 + -68x + 9x2 = 16 + -16 + 8x + -8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
84 + -68x + 9x2 = 0 + 8x + -8x + x2 + -1x2
84 + -68x + 9x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
84 + -68x + 9x2 = 0 + x2 + -1x2
84 + -68x + 9x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
84 + -68x + 9x2 = 0

Factor a trinomial.
(14 + -9x)(6 + -1x) = 0


Subproblem 1
Set the factor '(14 + -9x)' equal to zero and attempt to solve:

Simplifying
14 + -9x = 0

Solving
14 + -9x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -9x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -9x = 0 + -14
-9x = 0 + -14

Combine like terms: 0 + -14 = -14
-9x = -14

Divide each side by '-9'.
x = 1.555555556

Simplifying
x = 1.555555556

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {1.555555556, 6}

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