x(5x+7)=2x^2-7x+24

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Solution for x(5x+7)=2x^2-7x+24 equation: 


Simplifying
x(5x + 7) = 2x2 + -7x + 24

Reorder the terms:
x(7 + 5x) = 2x2 + -7x + 24
(7 * x + 5x * x) = 2x2 + -7x + 24
(7x + 5x2) = 2x2 + -7x + 24

Reorder the terms:
7x + 5x2 = 24 + -7x + 2x2

Solving
7x + 5x2 = 24 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-24 + 7x + 7x + 5x2 + -2x2 = 24 + -7x + 2x2 + -24 + 7x + -2x2

Combine like terms: 7x + 7x = 14x
-24 + 14x + 5x2 + -2x2 = 24 + -7x + 2x2 + -24 + 7x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-24 + 14x + 3x2 = 24 + -7x + 2x2 + -24 + 7x + -2x2

Reorder the terms:
-24 + 14x + 3x2 = 24 + -24 + -7x + 7x + 2x2 + -2x2

Combine like terms: 24 + -24 = 0
-24 + 14x + 3x2 = 0 + -7x + 7x + 2x2 + -2x2
-24 + 14x + 3x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-24 + 14x + 3x2 = 0 + 2x2 + -2x2
-24 + 14x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-24 + 14x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-6, 1.333333333}

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