-x^2+40x+2=4x^2+6x-5

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Solution for -x^2+40x+2=4x^2+6x-5 equation: 


Simplifying
-1x2 + 40x + 2 = 4x2 + 6x + -5

Reorder the terms:
2 + 40x + -1x2 = 4x2 + 6x + -5

Reorder the terms:
2 + 40x + -1x2 = -5 + 6x + 4x2

Solving
2 + 40x + -1x2 = -5 + 6x + 4x2

Solving for variable 'x'.

Reorder the terms:
2 + 5 + 40x + -6x + -1x2 + -4x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Combine like terms: 2 + 5 = 7
7 + 40x + -6x + -1x2 + -4x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Combine like terms: 40x + -6x = 34x
7 + 34x + -1x2 + -4x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Combine like terms: -1x2 + -4x2 = -5x2
7 + 34x + -5x2 = -5 + 6x + 4x2 + 5 + -6x + -4x2

Reorder the terms:
7 + 34x + -5x2 = -5 + 5 + 6x + -6x + 4x2 + -4x2

Combine like terms: -5 + 5 = 0
7 + 34x + -5x2 = 0 + 6x + -6x + 4x2 + -4x2
7 + 34x + -5x2 = 6x + -6x + 4x2 + -4x2

Combine like terms: 6x + -6x = 0
7 + 34x + -5x2 = 0 + 4x2 + -4x2
7 + 34x + -5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
7 + 34x + -5x2 = 0

Factor a trinomial.
(7 + -1x)(1 + 5x) = 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 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {7, -0.2}

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