((4x-9)(4x-9))-25=0

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Solution for ((4x-9)(4x-9))-25=0 equation: 


Simplifying
((4x + -9)(4x + -9)) + -25 = 0

Reorder the terms:
((-9 + 4x)(4x + -9)) + -25 = 0

Reorder the terms:
((-9 + 4x)(-9 + 4x)) + -25 = 0

Multiply (-9 + 4x) * (-9 + 4x)
((-9(-9 + 4x) + 4x * (-9 + 4x))) + -25 = 0
(((-9 * -9 + 4x * -9) + 4x * (-9 + 4x))) + -25 = 0
(((81 + -36x) + 4x * (-9 + 4x))) + -25 = 0
((81 + -36x + (-9 * 4x + 4x * 4x))) + -25 = 0
((81 + -36x + (-36x + 16x2))) + -25 = 0

Combine like terms: -36x + -36x = -72x
((81 + -72x + 16x2)) + -25 = 0
(81 + -72x + 16x2) + -25 = 0

Remove parenthesis around (81 + -72x + 16x2)
81 + -72x + 16x2 + -25 = 0

Reorder the terms:
81 + -25 + -72x + 16x2 = 0

Combine like terms: 81 + -25 = 56
56 + -72x + 16x2 = 0

Solving
56 + -72x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(7 + -9x + 2x2) = 0

Factor a trinomial.
8((1 + -1x)(7 + -2x)) = 0

Ignore the factor 8.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {1, 3.5}

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