(9-4x)*(9-5x)-4*(5-x)*(4x-5)-36*(4-4x+x^2)=0

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Solution for (9-4x)*(9-5x)-4*(5-x)*(4x-5)-36*(4-4x+x^2)=0 equation: 


Simplifying
(9 + -4x)(9 + -5x) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0

Multiply (9 + -4x) * (9 + -5x)
(9(9 + -5x) + -4x * (9 + -5x)) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0
((9 * 9 + -5x * 9) + -4x * (9 + -5x)) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0
((81 + -45x) + -4x * (9 + -5x)) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0
(81 + -45x + (9 * -4x + -5x * -4x)) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0
(81 + -45x + (-36x + 20x2)) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0

Combine like terms: -45x + -36x = -81x
(81 + -81x + 20x2) + -4(5 + -1x)(4x + -5) + -36(4 + -4x + x2) = 0

Reorder the terms:
81 + -81x + 20x2 + -4(5 + -1x)(-5 + 4x) + -36(4 + -4x + x2) = 0

Multiply (5 + -1x) * (-5 + 4x)
81 + -81x + 20x2 + -4(5(-5 + 4x) + -1x * (-5 + 4x)) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + -4((-5 * 5 + 4x * 5) + -1x * (-5 + 4x)) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + -4((-25 + 20x) + -1x * (-5 + 4x)) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + -4(-25 + 20x + (-5 * -1x + 4x * -1x)) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + -4(-25 + 20x + (5x + -4x2)) + -36(4 + -4x + x2) = 0

Combine like terms: 20x + 5x = 25x
81 + -81x + 20x2 + -4(-25 + 25x + -4x2) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + (-25 * -4 + 25x * -4 + -4x2 * -4) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + (100 + -100x + 16x2) + -36(4 + -4x + x2) = 0
81 + -81x + 20x2 + 100 + -100x + 16x2 + (4 * -36 + -4x * -36 + x2 * -36) = 0
81 + -81x + 20x2 + 100 + -100x + 16x2 + (-144 + 144x + -36x2) = 0

Reorder the terms:
81 + 100 + -144 + -81x + -100x + 144x + 20x2 + 16x2 + -36x2 = 0

Combine like terms: 81 + 100 = 181
181 + -144 + -81x + -100x + 144x + 20x2 + 16x2 + -36x2 = 0

Combine like terms: 181 + -144 = 37
37 + -81x + -100x + 144x + 20x2 + 16x2 + -36x2 = 0

Combine like terms: -81x + -100x = -181x
37 + -181x + 144x + 20x2 + 16x2 + -36x2 = 0

Combine like terms: -181x + 144x = -37x
37 + -37x + 20x2 + 16x2 + -36x2 = 0

Combine like terms: 20x2 + 16x2 = 36x2
37 + -37x + 36x2 + -36x2 = 0

Combine like terms: 36x2 + -36x2 = 0
37 + -37x + 0 = 0
37 + -37x = 0

Solving
37 + -37x = 0

Solving for variable 'x'.

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

Add '-37' to each side of the equation.
37 + -37 + -37x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -37x = 0 + -37
-37x = 0 + -37

Combine like terms: 0 + -37 = -37
-37x = -37

Divide each side by '-37'.
x = 1

Simplifying
x = 1

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