4x^2-5x-1=7x+6

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Solution for 4x^2-5x-1=7x+6 equation: 


Simplifying
4x2 + -5x + -1 = 7x + 6

Reorder the terms:
-1 + -5x + 4x2 = 7x + 6

Reorder the terms:
-1 + -5x + 4x2 = 6 + 7x

Solving
-1 + -5x + 4x2 = 6 + 7x

Solving for variable 'x'.

Reorder the terms:
-1 + -6 + -5x + -7x + 4x2 = 6 + 7x + -6 + -7x

Combine like terms: -1 + -6 = -7
-7 + -5x + -7x + 4x2 = 6 + 7x + -6 + -7x

Combine like terms: -5x + -7x = -12x
-7 + -12x + 4x2 = 6 + 7x + -6 + -7x

Reorder the terms:
-7 + -12x + 4x2 = 6 + -6 + 7x + -7x

Combine like terms: 6 + -6 = 0
-7 + -12x + 4x2 = 0 + 7x + -7x
-7 + -12x + 4x2 = 7x + -7x

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

Factor a trinomial.
(-1 + -2x)(7 + -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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-0.5, 3.5}

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