4x^2-13x+34=8x+7

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Solution for 4x^2-13x+34=8x+7 equation: 


Simplifying
4x2 + -13x + 34 = 8x + 7

Reorder the terms:
34 + -13x + 4x2 = 8x + 7

Reorder the terms:
34 + -13x + 4x2 = 7 + 8x

Solving
34 + -13x + 4x2 = 7 + 8x

Solving for variable 'x'.

Reorder the terms:
34 + -7 + -13x + -8x + 4x2 = 7 + 8x + -7 + -8x

Combine like terms: 34 + -7 = 27
27 + -13x + -8x + 4x2 = 7 + 8x + -7 + -8x

Combine like terms: -13x + -8x = -21x
27 + -21x + 4x2 = 7 + 8x + -7 + -8x

Reorder the terms:
27 + -21x + 4x2 = 7 + -7 + 8x + -8x

Combine like terms: 7 + -7 = 0
27 + -21x + 4x2 = 0 + 8x + -8x
27 + -21x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
27 + -21x + 4x2 = 0

Factor a trinomial.
(9 + -4x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2.25, 3}

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