4x^2-5x+13=3x+10

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Solution for 4x^2-5x+13=3x+10 equation: 


Simplifying
4x2 + -5x + 13 = 3x + 10

Reorder the terms:
13 + -5x + 4x2 = 3x + 10

Reorder the terms:
13 + -5x + 4x2 = 10 + 3x

Solving
13 + -5x + 4x2 = 10 + 3x

Solving for variable 'x'.

Reorder the terms:
13 + -10 + -5x + -3x + 4x2 = 10 + 3x + -10 + -3x

Combine like terms: 13 + -10 = 3
3 + -5x + -3x + 4x2 = 10 + 3x + -10 + -3x

Combine like terms: -5x + -3x = -8x
3 + -8x + 4x2 = 10 + 3x + -10 + -3x

Reorder the terms:
3 + -8x + 4x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
3 + -8x + 4x2 = 0 + 3x + -3x
3 + -8x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
3 + -8x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(3 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0.5, 1.5}

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