3x^2-41x=-4x^2-7x-24

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Solution for 3x^2-41x=-4x^2-7x-24 equation: 


Simplifying
3x2 + -41x = -4x2 + -7x + -24

Reorder the terms:
-41x + 3x2 = -4x2 + -7x + -24

Reorder the terms:
-41x + 3x2 = -24 + -7x + -4x2

Solving
-41x + 3x2 = -24 + -7x + -4x2

Solving for variable 'x'.

Reorder the terms:
24 + -41x + 7x + 3x2 + 4x2 = -24 + -7x + -4x2 + 24 + 7x + 4x2

Combine like terms: -41x + 7x = -34x
24 + -34x + 3x2 + 4x2 = -24 + -7x + -4x2 + 24 + 7x + 4x2

Combine like terms: 3x2 + 4x2 = 7x2
24 + -34x + 7x2 = -24 + -7x + -4x2 + 24 + 7x + 4x2

Reorder the terms:
24 + -34x + 7x2 = -24 + 24 + -7x + 7x + -4x2 + 4x2

Combine like terms: -24 + 24 = 0
24 + -34x + 7x2 = 0 + -7x + 7x + -4x2 + 4x2
24 + -34x + 7x2 = -7x + 7x + -4x2 + 4x2

Combine like terms: -7x + 7x = 0
24 + -34x + 7x2 = 0 + -4x2 + 4x2
24 + -34x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
24 + -34x + 7x2 = 0

Factor a trinomial.
(6 + -7x)(4 + -1x) = 0


Subproblem 1
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0.8571428571, 4}

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