4x^2+x-5=5x+30

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Solution for 4x^2+x-5=5x+30 equation: 


Simplifying
4x2 + x + -5 = 5x + 30

Reorder the terms:
-5 + x + 4x2 = 5x + 30

Reorder the terms:
-5 + x + 4x2 = 30 + 5x

Solving
-5 + x + 4x2 = 30 + 5x

Solving for variable 'x'.

Reorder the terms:
-5 + -30 + x + -5x + 4x2 = 30 + 5x + -30 + -5x

Combine like terms: -5 + -30 = -35
-35 + x + -5x + 4x2 = 30 + 5x + -30 + -5x

Combine like terms: x + -5x = -4x
-35 + -4x + 4x2 = 30 + 5x + -30 + -5x

Reorder the terms:
-35 + -4x + 4x2 = 30 + -30 + 5x + -5x

Combine like terms: 30 + -30 = 0
-35 + -4x + 4x2 = 0 + 5x + -5x
-35 + -4x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-35 + -4x + 4x2 = 0

Factor a trinomial.
(-5 + -2x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-2.5, 3.5}

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