5x^2-3x-41=(3x-7)*(3x-7)

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Solution for 5x^2-3x-41=(3x-7)*(3x-7) equation: 


Simplifying
5x2 + -3x + -41 = (3x + -7)(3x + -7)

Reorder the terms:
-41 + -3x + 5x2 = (3x + -7)(3x + -7)

Reorder the terms:
-41 + -3x + 5x2 = (-7 + 3x)(3x + -7)

Reorder the terms:
-41 + -3x + 5x2 = (-7 + 3x)(-7 + 3x)

Multiply (-7 + 3x) * (-7 + 3x)
-41 + -3x + 5x2 = (-7(-7 + 3x) + 3x * (-7 + 3x))
-41 + -3x + 5x2 = ((-7 * -7 + 3x * -7) + 3x * (-7 + 3x))
-41 + -3x + 5x2 = ((49 + -21x) + 3x * (-7 + 3x))
-41 + -3x + 5x2 = (49 + -21x + (-7 * 3x + 3x * 3x))
-41 + -3x + 5x2 = (49 + -21x + (-21x + 9x2))

Combine like terms: -21x + -21x = -42x
-41 + -3x + 5x2 = (49 + -42x + 9x2)

Solving
-41 + -3x + 5x2 = 49 + -42x + 9x2

Solving for variable 'x'.

Reorder the terms:
-41 + -49 + -3x + 42x + 5x2 + -9x2 = 49 + -42x + 9x2 + -49 + 42x + -9x2

Combine like terms: -41 + -49 = -90
-90 + -3x + 42x + 5x2 + -9x2 = 49 + -42x + 9x2 + -49 + 42x + -9x2

Combine like terms: -3x + 42x = 39x
-90 + 39x + 5x2 + -9x2 = 49 + -42x + 9x2 + -49 + 42x + -9x2

Combine like terms: 5x2 + -9x2 = -4x2
-90 + 39x + -4x2 = 49 + -42x + 9x2 + -49 + 42x + -9x2

Reorder the terms:
-90 + 39x + -4x2 = 49 + -49 + -42x + 42x + 9x2 + -9x2

Combine like terms: 49 + -49 = 0
-90 + 39x + -4x2 = 0 + -42x + 42x + 9x2 + -9x2
-90 + 39x + -4x2 = -42x + 42x + 9x2 + -9x2

Combine like terms: -42x + 42x = 0
-90 + 39x + -4x2 = 0 + 9x2 + -9x2
-90 + 39x + -4x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-90 + 39x + -4x2 = 0

Factor a trinomial.
(-6 + x)(15 + -4x) = 0


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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6

Subproblem 2
Set the factor '(15 + -4x)' equal to zero and attempt to solve:

Simplifying
15 + -4x = 0

Solving
15 + -4x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4x = 0 + -15
-4x = 0 + -15

Combine like terms: 0 + -15 = -15
-4x = -15

Divide each side by '-4'.
x = 3.75

Simplifying
x = 3.75
Solution
x = {6, 3.75}

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