4x^2+10x-6=24-9x

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Solution for 4x^2+10x-6=24-9x equation: 


Simplifying
4x2 + 10x + -6 = 24 + -9x

Reorder the terms:
-6 + 10x + 4x2 = 24 + -9x

Solving
-6 + 10x + 4x2 = 24 + -9x

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 10x + 9x + 4x2 = 24 + -9x + -24 + 9x

Combine like terms: -6 + -24 = -30
-30 + 10x + 9x + 4x2 = 24 + -9x + -24 + 9x

Combine like terms: 10x + 9x = 19x
-30 + 19x + 4x2 = 24 + -9x + -24 + 9x

Reorder the terms:
-30 + 19x + 4x2 = 24 + -24 + -9x + 9x

Combine like terms: 24 + -24 = 0
-30 + 19x + 4x2 = 0 + -9x + 9x
-30 + 19x + 4x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-30 + 19x + 4x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -4x) = 0


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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-6, 1.25}

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