-4x^2-14x+40=-5x^2-2x+5

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Solution for -4x^2-14x+40=-5x^2-2x+5 equation:


Simplifying
-4x2 + -14x + 40 = -5x2 + -2x + 5

Reorder the terms:
40 + -14x + -4x2 = -5x2 + -2x + 5

Reorder the terms:
40 + -14x + -4x2 = 5 + -2x + -5x2

Solving
40 + -14x + -4x2 = 5 + -2x + -5x2

Solving for variable 'x'.

Reorder the terms:
40 + -5 + -14x + 2x + -4x2 + 5x2 = 5 + -2x + -5x2 + -5 + 2x + 5x2

Combine like terms: 40 + -5 = 35
35 + -14x + 2x + -4x2 + 5x2 = 5 + -2x + -5x2 + -5 + 2x + 5x2

Combine like terms: -14x + 2x = -12x
35 + -12x + -4x2 + 5x2 = 5 + -2x + -5x2 + -5 + 2x + 5x2

Combine like terms: -4x2 + 5x2 = 1x2
35 + -12x + 1x2 = 5 + -2x + -5x2 + -5 + 2x + 5x2

Reorder the terms:
35 + -12x + 1x2 = 5 + -5 + -2x + 2x + -5x2 + 5x2

Combine like terms: 5 + -5 = 0
35 + -12x + 1x2 = 0 + -2x + 2x + -5x2 + 5x2
35 + -12x + 1x2 = -2x + 2x + -5x2 + 5x2

Combine like terms: -2x + 2x = 0
35 + -12x + 1x2 = 0 + -5x2 + 5x2
35 + -12x + 1x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
35 + -12x + 1x2 = 0

Factor a trinomial.
(5 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 7}

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