3x+10=25-20x+4x^2

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Solution for 3x+10=25-20x+4x^2 equation:


Simplifying
3x + 10 = 25 + -20x + 4x2

Reorder the terms:
10 + 3x = 25 + -20x + 4x2

Solving
10 + 3x = 25 + -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
10 + -25 + 3x + 20x + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2

Combine like terms: 10 + -25 = -15
-15 + 3x + 20x + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2

Combine like terms: 3x + 20x = 23x
-15 + 23x + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2

Reorder the terms:
-15 + 23x + -4x2 = 25 + -25 + -20x + 20x + 4x2 + -4x2

Combine like terms: 25 + -25 = 0
-15 + 23x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2
-15 + 23x + -4x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-15 + 23x + -4x2 = 0 + 4x2 + -4x2
-15 + 23x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-15 + 23x + -4x2 = 0

Factor a trinomial.
(-5 + x)(3 + -4x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {5, 0.75}

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