4x+5=4x^2-20x+25

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Solution for 4x+5=4x^2-20x+25 equation: 


Simplifying
4x + 5 = 4x2 + -20x + 25

Reorder the terms:
5 + 4x = 4x2 + -20x + 25

Reorder the terms:
5 + 4x = 25 + -20x + 4x2

Solving
5 + 4x = 25 + -20x + 4x2

Solving for variable 'x'.

Reorder the terms:
5 + -25 + 4x + 20x + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2

Combine like terms: 5 + -25 = -20
-20 + 4x + 20x + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2

Combine like terms: 4x + 20x = 24x
-20 + 24x + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2

Reorder the terms:
-20 + 24x + -4x2 = 25 + -25 + -20x + 20x + 4x2 + -4x2

Combine like terms: 25 + -25 = 0
-20 + 24x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2
-20 + 24x + -4x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-20 + 24x + -4x2 = 0 + 4x2 + -4x2
-20 + 24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-20 + 24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 6x + -1x2) = 0

Factor a trinomial.
4((-5 + x)(1 + -1x)) = 0

Ignore the factor 4.

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 '(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 = {5, 1}

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