(4*x-2)*(7*x+12)+(2-4*x)*(13-25*x)=0

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Solution for (4*x-2)*(7*x+12)+(2-4*x)*(13-25*x)=0 equation: 


Simplifying
(4x + -2)(7x + 12) + (2 + -4x)(13 + -25x) = 0

Reorder the terms:
(-2 + 4x)(7x + 12) + (2 + -4x)(13 + -25x) = 0

Reorder the terms:
(-2 + 4x)(12 + 7x) + (2 + -4x)(13 + -25x) = 0

Multiply (-2 + 4x) * (12 + 7x)
(-2(12 + 7x) + 4x * (12 + 7x)) + (2 + -4x)(13 + -25x) = 0
((12 * -2 + 7x * -2) + 4x * (12 + 7x)) + (2 + -4x)(13 + -25x) = 0
((-24 + -14x) + 4x * (12 + 7x)) + (2 + -4x)(13 + -25x) = 0
(-24 + -14x + (12 * 4x + 7x * 4x)) + (2 + -4x)(13 + -25x) = 0
(-24 + -14x + (48x + 28x2)) + (2 + -4x)(13 + -25x) = 0

Combine like terms: -14x + 48x = 34x
(-24 + 34x + 28x2) + (2 + -4x)(13 + -25x) = 0

Multiply (2 + -4x) * (13 + -25x)
-24 + 34x + 28x2 + (2(13 + -25x) + -4x * (13 + -25x)) = 0
-24 + 34x + 28x2 + ((13 * 2 + -25x * 2) + -4x * (13 + -25x)) = 0
-24 + 34x + 28x2 + ((26 + -50x) + -4x * (13 + -25x)) = 0
-24 + 34x + 28x2 + (26 + -50x + (13 * -4x + -25x * -4x)) = 0
-24 + 34x + 28x2 + (26 + -50x + (-52x + 100x2)) = 0

Combine like terms: -50x + -52x = -102x
-24 + 34x + 28x2 + (26 + -102x + 100x2) = 0

Reorder the terms:
-24 + 26 + 34x + -102x + 28x2 + 100x2 = 0

Combine like terms: -24 + 26 = 2
2 + 34x + -102x + 28x2 + 100x2 = 0

Combine like terms: 34x + -102x = -68x
2 + -68x + 28x2 + 100x2 = 0

Combine like terms: 28x2 + 100x2 = 128x2
2 + -68x + 128x2 = 0

Solving
2 + -68x + 128x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -34x + 64x2) = 0

Factor a trinomial.
2((1 + -32x)(1 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -32x)' equal to zero and attempt to solve:

Simplifying
1 + -32x = 0

Solving
1 + -32x = 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 + -32x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -32x = 0 + -1
-32x = 0 + -1

Combine like terms: 0 + -1 = -1
-32x = -1

Divide each side by '-32'.
x = 0.03125

Simplifying
x = 0.03125

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.03125, 0.5}

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