4x^2-5x+13=7x+8

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Solution for 4x^2-5x+13=7x+8 equation: 


Simplifying
4x2 + -5x + 13 = 7x + 8

Reorder the terms:
13 + -5x + 4x2 = 7x + 8

Reorder the terms:
13 + -5x + 4x2 = 8 + 7x

Solving
13 + -5x + 4x2 = 8 + 7x

Solving for variable 'x'.

Reorder the terms:
13 + -8 + -5x + -7x + 4x2 = 8 + 7x + -8 + -7x

Combine like terms: 13 + -8 = 5
5 + -5x + -7x + 4x2 = 8 + 7x + -8 + -7x

Combine like terms: -5x + -7x = -12x
5 + -12x + 4x2 = 8 + 7x + -8 + -7x

Reorder the terms:
5 + -12x + 4x2 = 8 + -8 + 7x + -7x

Combine like terms: 8 + -8 = 0
5 + -12x + 4x2 = 0 + 7x + -7x
5 + -12x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
5 + -12x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(5 + -2x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
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
Solution
x = {0.5, 2.5}

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