4x^2+5x=36x+90

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Solution for 4x^2+5x=36x+90 equation: 


Simplifying
4x2 + 5x = 36x + 90

Reorder the terms:
5x + 4x2 = 36x + 90

Reorder the terms:
5x + 4x2 = 90 + 36x

Solving
5x + 4x2 = 90 + 36x

Solving for variable 'x'.

Reorder the terms:
-90 + 5x + -36x + 4x2 = 90 + 36x + -90 + -36x

Combine like terms: 5x + -36x = -31x
-90 + -31x + 4x2 = 90 + 36x + -90 + -36x

Reorder the terms:
-90 + -31x + 4x2 = 90 + -90 + 36x + -36x

Combine like terms: 90 + -90 = 0
-90 + -31x + 4x2 = 0 + 36x + -36x
-90 + -31x + 4x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-90 + -31x + 4x2 = 0

Factor a trinomial.
(-9 + -4x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-2.25, 10}

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