(25*16)-(25-2x)(16-2x)=148

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Solution for (25*16)-(25-2x)(16-2x)=148 equation: 


Simplifying
(25 * 16) + -1(25 + -2x)(16 + -2x) = 148

Multiply 25 * 16
(400) + -1(25 + -2x)(16 + -2x) = 148
400 + -1(25 + -2x)(16 + -2x) = 148

Multiply (25 + -2x) * (16 + -2x)
400 + -1(25(16 + -2x) + -2x * (16 + -2x)) = 148
400 + -1((16 * 25 + -2x * 25) + -2x * (16 + -2x)) = 148
400 + -1((400 + -50x) + -2x * (16 + -2x)) = 148
400 + -1(400 + -50x + (16 * -2x + -2x * -2x)) = 148
400 + -1(400 + -50x + (-32x + 4x2)) = 148

Combine like terms: -50x + -32x = -82x
400 + -1(400 + -82x + 4x2) = 148
400 + (400 * -1 + -82x * -1 + 4x2 * -1) = 148
400 + (-400 + 82x + -4x2) = 148

Combine like terms: 400 + -400 = 0
0 + 82x + -4x2 = 148
82x + -4x2 = 148

Solving
82x + -4x2 = 148

Solving for variable 'x'.

Reorder the terms:
-148 + 82x + -4x2 = 148 + -148

Combine like terms: 148 + -148 = 0
-148 + 82x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-74 + 41x + -2x2) = 0

Factor a trinomial.
2((-37 + 2x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-37 + 2x)' equal to zero and attempt to solve:

Simplifying
-37 + 2x = 0

Solving
-37 + 2x = 0

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

Add '37' to each side of the equation.
-37 + 37 + 2x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 2x = 0 + 37
2x = 0 + 37

Combine like terms: 0 + 37 = 37
2x = 37

Divide each side by '2'.
x = 18.5

Simplifying
x = 18.5

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {18.5, 2}

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