25(9x-2)*(9x-2)-4(5x-12)*(5x-12)=0

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Solution for 25(9x-2)*(9x-2)-4(5x-12)*(5x-12)=0 equation: 


Simplifying
25(9x + -2)(9x + -2) + -4(5x + -12)(5x + -12) = 0

Reorder the terms:
25(-2 + 9x)(9x + -2) + -4(5x + -12)(5x + -12) = 0

Reorder the terms:
25(-2 + 9x)(-2 + 9x) + -4(5x + -12)(5x + -12) = 0

Multiply (-2 + 9x) * (-2 + 9x)
25(-2(-2 + 9x) + 9x * (-2 + 9x)) + -4(5x + -12)(5x + -12) = 0
25((-2 * -2 + 9x * -2) + 9x * (-2 + 9x)) + -4(5x + -12)(5x + -12) = 0
25((4 + -18x) + 9x * (-2 + 9x)) + -4(5x + -12)(5x + -12) = 0
25(4 + -18x + (-2 * 9x + 9x * 9x)) + -4(5x + -12)(5x + -12) = 0
25(4 + -18x + (-18x + 81x2)) + -4(5x + -12)(5x + -12) = 0

Combine like terms: -18x + -18x = -36x
25(4 + -36x + 81x2) + -4(5x + -12)(5x + -12) = 0
(4 * 25 + -36x * 25 + 81x2 * 25) + -4(5x + -12)(5x + -12) = 0
(100 + -900x + 2025x2) + -4(5x + -12)(5x + -12) = 0

Reorder the terms:
100 + -900x + 2025x2 + -4(-12 + 5x)(5x + -12) = 0

Reorder the terms:
100 + -900x + 2025x2 + -4(-12 + 5x)(-12 + 5x) = 0

Multiply (-12 + 5x) * (-12 + 5x)
100 + -900x + 2025x2 + -4(-12(-12 + 5x) + 5x * (-12 + 5x)) = 0
100 + -900x + 2025x2 + -4((-12 * -12 + 5x * -12) + 5x * (-12 + 5x)) = 0
100 + -900x + 2025x2 + -4((144 + -60x) + 5x * (-12 + 5x)) = 0
100 + -900x + 2025x2 + -4(144 + -60x + (-12 * 5x + 5x * 5x)) = 0
100 + -900x + 2025x2 + -4(144 + -60x + (-60x + 25x2)) = 0

Combine like terms: -60x + -60x = -120x
100 + -900x + 2025x2 + -4(144 + -120x + 25x2) = 0
100 + -900x + 2025x2 + (144 * -4 + -120x * -4 + 25x2 * -4) = 0
100 + -900x + 2025x2 + (-576 + 480x + -100x2) = 0

Reorder the terms:
100 + -576 + -900x + 480x + 2025x2 + -100x2 = 0

Combine like terms: 100 + -576 = -476
-476 + -900x + 480x + 2025x2 + -100x2 = 0

Combine like terms: -900x + 480x = -420x
-476 + -420x + 2025x2 + -100x2 = 0

Combine like terms: 2025x2 + -100x2 = 1925x2
-476 + -420x + 1925x2 = 0

Solving
-476 + -420x + 1925x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-68 + -60x + 275x2) = 0

Factor a trinomial.
7((-2 + -5x)(34 + -55x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
Set the factor '(34 + -55x)' equal to zero and attempt to solve:

Simplifying
34 + -55x = 0

Solving
34 + -55x = 0

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

Add '-34' to each side of the equation.
34 + -34 + -55x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -55x = 0 + -34
-55x = 0 + -34

Combine like terms: 0 + -34 = -34
-55x = -34

Divide each side by '-55'.
x = 0.6181818182

Simplifying
x = 0.6181818182
Solution
x = {-0.4, 0.6181818182}

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