(x-3)*(x-3)=(2x-7)*(2x-7)

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


Simplifying
(x + -3)(x + -3) = (2x + -7)(2x + -7)

Reorder the terms:
(-3 + x)(x + -3) = (2x + -7)(2x + -7)

Reorder the terms:
(-3 + x)(-3 + x) = (2x + -7)(2x + -7)

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = (2x + -7)(2x + -7)
((-3 * -3 + x * -3) + x(-3 + x)) = (2x + -7)(2x + -7)
((9 + -3x) + x(-3 + x)) = (2x + -7)(2x + -7)
(9 + -3x + (-3 * x + x * x)) = (2x + -7)(2x + -7)
(9 + -3x + (-3x + x2)) = (2x + -7)(2x + -7)

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = (2x + -7)(2x + -7)

Reorder the terms:
9 + -6x + x2 = (-7 + 2x)(2x + -7)

Reorder the terms:
9 + -6x + x2 = (-7 + 2x)(-7 + 2x)

Multiply (-7 + 2x) * (-7 + 2x)
9 + -6x + x2 = (-7(-7 + 2x) + 2x * (-7 + 2x))
9 + -6x + x2 = ((-7 * -7 + 2x * -7) + 2x * (-7 + 2x))
9 + -6x + x2 = ((49 + -14x) + 2x * (-7 + 2x))
9 + -6x + x2 = (49 + -14x + (-7 * 2x + 2x * 2x))
9 + -6x + x2 = (49 + -14x + (-14x + 4x2))

Combine like terms: -14x + -14x = -28x
9 + -6x + x2 = (49 + -28x + 4x2)

Solving
9 + -6x + x2 = 49 + -28x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + -49 + -6x + 28x + x2 + -4x2 = 49 + -28x + 4x2 + -49 + 28x + -4x2

Combine like terms: 9 + -49 = -40
-40 + -6x + 28x + x2 + -4x2 = 49 + -28x + 4x2 + -49 + 28x + -4x2

Combine like terms: -6x + 28x = 22x
-40 + 22x + x2 + -4x2 = 49 + -28x + 4x2 + -49 + 28x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-40 + 22x + -3x2 = 49 + -28x + 4x2 + -49 + 28x + -4x2

Reorder the terms:
-40 + 22x + -3x2 = 49 + -49 + -28x + 28x + 4x2 + -4x2

Combine like terms: 49 + -49 = 0
-40 + 22x + -3x2 = 0 + -28x + 28x + 4x2 + -4x2
-40 + 22x + -3x2 = -28x + 28x + 4x2 + -4x2

Combine like terms: -28x + 28x = 0
-40 + 22x + -3x2 = 0 + 4x2 + -4x2
-40 + 22x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-40 + 22x + -3x2 = 0

Factor a trinomial.
(-4 + x)(10 + -3x) = 0


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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4

Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333
Solution
x = {4, 3.333333333}

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