2x^2+19x=6x+7

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Solution for 2x^2+19x=6x+7 equation: 


Simplifying
2x2 + 19x = 6x + 7

Reorder the terms:
19x + 2x2 = 6x + 7

Reorder the terms:
19x + 2x2 = 7 + 6x

Solving
19x + 2x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
-7 + 19x + -6x + 2x2 = 7 + 6x + -7 + -6x

Combine like terms: 19x + -6x = 13x
-7 + 13x + 2x2 = 7 + 6x + -7 + -6x

Reorder the terms:
-7 + 13x + 2x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
-7 + 13x + 2x2 = 0 + 6x + -6x
-7 + 13x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-7 + 13x + 2x2 = 0

Factor a trinomial.
(-7 + -1x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
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
Solution
x = {-7, 0.5}

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