28x-74=4x^2-25

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Solution for 28x-74=4x^2-25 equation: 


Simplifying
28x + -74 = 4x2 + -25

Reorder the terms:
-74 + 28x = 4x2 + -25

Reorder the terms:
-74 + 28x = -25 + 4x2

Solving
-74 + 28x = -25 + 4x2

Solving for variable 'x'.

Reorder the terms:
-74 + 25 + 28x + -4x2 = -25 + 4x2 + 25 + -4x2

Combine like terms: -74 + 25 = -49
-49 + 28x + -4x2 = -25 + 4x2 + 25 + -4x2

Reorder the terms:
-49 + 28x + -4x2 = -25 + 25 + 4x2 + -4x2

Combine like terms: -25 + 25 = 0
-49 + 28x + -4x2 = 0 + 4x2 + -4x2
-49 + 28x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-49 + 28x + -4x2 = 0

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


Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {3.5, 3.5}

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