7x+67=4x^2+20x+25

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Solution for 7x+67=4x^2+20x+25 equation: 


Simplifying
7x + 67 = 4x2 + 20x + 25

Reorder the terms:
67 + 7x = 4x2 + 20x + 25

Reorder the terms:
67 + 7x = 25 + 20x + 4x2

Solving
67 + 7x = 25 + 20x + 4x2

Solving for variable 'x'.

Reorder the terms:
67 + -25 + 7x + -20x + -4x2 = 25 + 20x + 4x2 + -25 + -20x + -4x2

Combine like terms: 67 + -25 = 42
42 + 7x + -20x + -4x2 = 25 + 20x + 4x2 + -25 + -20x + -4x2

Combine like terms: 7x + -20x = -13x
42 + -13x + -4x2 = 25 + 20x + 4x2 + -25 + -20x + -4x2

Reorder the terms:
42 + -13x + -4x2 = 25 + -25 + 20x + -20x + 4x2 + -4x2

Combine like terms: 25 + -25 = 0
42 + -13x + -4x2 = 0 + 20x + -20x + 4x2 + -4x2
42 + -13x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
42 + -13x + -4x2 = 0 + 4x2 + -4x2
42 + -13x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
42 + -13x + -4x2 = 0

Factor a trinomial.
(2 + -1x)(21 + 4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(21 + 4x)' equal to zero and attempt to solve:

Simplifying
21 + 4x = 0

Solving
21 + 4x = 0

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

Add '-21' to each side of the equation.
21 + -21 + 4x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4x = 0 + -21
4x = 0 + -21

Combine like terms: 0 + -21 = -21
4x = -21

Divide each side by '4'.
x = -5.25

Simplifying
x = -5.25
Solution
x = {2, -5.25}

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