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

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


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

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

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

Solving for variable 'x'.

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

Combine like terms: -7 + -1 = -8
-8 + -4x + x + 5x2 = 1 + -1x + -1 + x

Combine like terms: -4x + x = -3x
-8 + -3x + 5x2 = 1 + -1x + -1 + x

Reorder the terms:
-8 + -3x + 5x2 = 1 + -1 + -1x + x

Combine like terms: 1 + -1 = 0
-8 + -3x + 5x2 = 0 + -1x + x
-8 + -3x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-8 + -3x + 5x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -5x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-1, 1.6}

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