4x^2-13x+19=7x+10

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Solution for 4x^2-13x+19=7x+10 equation: 


Simplifying
4x2 + -13x + 19 = 7x + 10

Reorder the terms:
19 + -13x + 4x2 = 7x + 10

Reorder the terms:
19 + -13x + 4x2 = 10 + 7x

Solving
19 + -13x + 4x2 = 10 + 7x

Solving for variable 'x'.

Reorder the terms:
19 + -10 + -13x + -7x + 4x2 = 10 + 7x + -10 + -7x

Combine like terms: 19 + -10 = 9
9 + -13x + -7x + 4x2 = 10 + 7x + -10 + -7x

Combine like terms: -13x + -7x = -20x
9 + -20x + 4x2 = 10 + 7x + -10 + -7x

Reorder the terms:
9 + -20x + 4x2 = 10 + -10 + 7x + -7x

Combine like terms: 10 + -10 = 0
9 + -20x + 4x2 = 0 + 7x + -7x
9 + -20x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
9 + -20x + 4x2 = 0

Factor a trinomial.
(1 + -2x)(9 + -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 '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {0.5, 4.5}

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