12-(2x-5)(2x-5)=3x

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Solution for 12-(2x-5)(2x-5)=3x equation: 


Simplifying
12 + -1(2x + -5)(2x + -5) = 3x

Reorder the terms:
12 + -1(-5 + 2x)(2x + -5) = 3x

Reorder the terms:
12 + -1(-5 + 2x)(-5 + 2x) = 3x

Multiply (-5 + 2x) * (-5 + 2x)
12 + -1(-5(-5 + 2x) + 2x * (-5 + 2x)) = 3x
12 + -1((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) = 3x
12 + -1((25 + -10x) + 2x * (-5 + 2x)) = 3x
12 + -1(25 + -10x + (-5 * 2x + 2x * 2x)) = 3x
12 + -1(25 + -10x + (-10x + 4x2)) = 3x

Combine like terms: -10x + -10x = -20x
12 + -1(25 + -20x + 4x2) = 3x
12 + (25 * -1 + -20x * -1 + 4x2 * -1) = 3x
12 + (-25 + 20x + -4x2) = 3x

Combine like terms: 12 + -25 = -13
-13 + 20x + -4x2 = 3x

Solving
-13 + 20x + -4x2 = 3x

Solving for variable 'x'.

Reorder the terms:
-13 + 20x + -3x + -4x2 = 3x + -3x

Combine like terms: 20x + -3x = 17x
-13 + 17x + -4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-13 + 17x + -4x2 = 0

Factor a trinomial.
(-13 + 4x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-13 + 4x)' equal to zero and attempt to solve:

Simplifying
-13 + 4x = 0

Solving
-13 + 4x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 4x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 4x = 0 + 13
4x = 0 + 13

Combine like terms: 0 + 13 = 13
4x = 13

Divide each side by '4'.
x = 3.25

Simplifying
x = 3.25

Subproblem 2
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
Solution
x = {3.25, 1}

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