4x^2-27x+52=2x+7

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Solution for 4x^2-27x+52=2x+7 equation: 


Simplifying
4x2 + -27x + 52 = 2x + 7

Reorder the terms:
52 + -27x + 4x2 = 2x + 7

Reorder the terms:
52 + -27x + 4x2 = 7 + 2x

Solving
52 + -27x + 4x2 = 7 + 2x

Solving for variable 'x'.

Reorder the terms:
52 + -7 + -27x + -2x + 4x2 = 7 + 2x + -7 + -2x

Combine like terms: 52 + -7 = 45
45 + -27x + -2x + 4x2 = 7 + 2x + -7 + -2x

Combine like terms: -27x + -2x = -29x
45 + -29x + 4x2 = 7 + 2x + -7 + -2x

Reorder the terms:
45 + -29x + 4x2 = 7 + -7 + 2x + -2x

Combine like terms: 7 + -7 = 0
45 + -29x + 4x2 = 0 + 2x + -2x
45 + -29x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
45 + -29x + 4x2 = 0

Factor a trinomial.
(9 + -4x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2.25, 5}

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