7x-7=(2x-9)(2x-9)

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Solution for 7x-7=(2x-9)(2x-9) equation: 


Simplifying
7x + -7 = (2x + -9)(2x + -9)

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

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

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

Multiply (-9 + 2x) * (-9 + 2x)
-7 + 7x = (-9(-9 + 2x) + 2x * (-9 + 2x))
-7 + 7x = ((-9 * -9 + 2x * -9) + 2x * (-9 + 2x))
-7 + 7x = ((81 + -18x) + 2x * (-9 + 2x))
-7 + 7x = (81 + -18x + (-9 * 2x + 2x * 2x))
-7 + 7x = (81 + -18x + (-18x + 4x2))

Combine like terms: -18x + -18x = -36x
-7 + 7x = (81 + -36x + 4x2)

Solving
-7 + 7x = 81 + -36x + 4x2

Solving for variable 'x'.

Reorder the terms:
-7 + -81 + 7x + 36x + -4x2 = 81 + -36x + 4x2 + -81 + 36x + -4x2

Combine like terms: -7 + -81 = -88
-88 + 7x + 36x + -4x2 = 81 + -36x + 4x2 + -81 + 36x + -4x2

Combine like terms: 7x + 36x = 43x
-88 + 43x + -4x2 = 81 + -36x + 4x2 + -81 + 36x + -4x2

Reorder the terms:
-88 + 43x + -4x2 = 81 + -81 + -36x + 36x + 4x2 + -4x2

Combine like terms: 81 + -81 = 0
-88 + 43x + -4x2 = 0 + -36x + 36x + 4x2 + -4x2
-88 + 43x + -4x2 = -36x + 36x + 4x2 + -4x2

Combine like terms: -36x + 36x = 0
-88 + 43x + -4x2 = 0 + 4x2 + -4x2
-88 + 43x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-88 + 43x + -4x2 = 0

Factor a trinomial.
(-8 + x)(11 + -4x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {8, 2.75}

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