4x^2-7x+19=8x+5

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Solution for 4x^2-7x+19=8x+5 equation: 


Simplifying
4x2 + -7x + 19 = 8x + 5

Reorder the terms:
19 + -7x + 4x2 = 8x + 5

Reorder the terms:
19 + -7x + 4x2 = 5 + 8x

Solving
19 + -7x + 4x2 = 5 + 8x

Solving for variable 'x'.

Reorder the terms:
19 + -5 + -7x + -8x + 4x2 = 5 + 8x + -5 + -8x

Combine like terms: 19 + -5 = 14
14 + -7x + -8x + 4x2 = 5 + 8x + -5 + -8x

Combine like terms: -7x + -8x = -15x
14 + -15x + 4x2 = 5 + 8x + -5 + -8x

Reorder the terms:
14 + -15x + 4x2 = 5 + -5 + 8x + -8x

Combine like terms: 5 + -5 = 0
14 + -15x + 4x2 = 0 + 8x + -8x
14 + -15x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
14 + -15x + 4x2 = 0

Factor a trinomial.
(7 + -4x)(2 + -1x) = 0


Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.75, 2}

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