4x^2+20x+25=x+13

Solution for 4x^2+20x+25=x+13 equation:

Simplifying
4x2 + 20x + 25 = x + 13

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

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

Solving
25 + 20x + 4x2 = 13 + x

Solving for variable 'x'.

Reorder the terms:
25 + -13 + 20x + -1x + 4x2 = 13 + x + -13 + -1x

Combine like terms: 25 + -13 = 12
12 + 20x + -1x + 4x2 = 13 + x + -13 + -1x

Combine like terms: 20x + -1x = 19x
12 + 19x + 4x2 = 13 + x + -13 + -1x

Reorder the terms:
12 + 19x + 4x2 = 13 + -13 + x + -1x

Combine like terms: 13 + -13 = 0
12 + 19x + 4x2 = 0 + x + -1x
12 + 19x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
12 + 19x + 4x2 = 0

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

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4
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 = {-4, -0.75}