x(5x+8)=2x^2-12x+7

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Solution for x(5x+8)=2x^2-12x+7 equation: 


Simplifying
x(5x + 8) = 2x2 + -12x + 7

Reorder the terms:
x(8 + 5x) = 2x2 + -12x + 7
(8 * x + 5x * x) = 2x2 + -12x + 7
(8x + 5x2) = 2x2 + -12x + 7

Reorder the terms:
8x + 5x2 = 7 + -12x + 2x2

Solving
8x + 5x2 = 7 + -12x + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + 8x + 12x + 5x2 + -2x2 = 7 + -12x + 2x2 + -7 + 12x + -2x2

Combine like terms: 8x + 12x = 20x
-7 + 20x + 5x2 + -2x2 = 7 + -12x + 2x2 + -7 + 12x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-7 + 20x + 3x2 = 7 + -12x + 2x2 + -7 + 12x + -2x2

Reorder the terms:
-7 + 20x + 3x2 = 7 + -7 + -12x + 12x + 2x2 + -2x2

Combine like terms: 7 + -7 = 0
-7 + 20x + 3x2 = 0 + -12x + 12x + 2x2 + -2x2
-7 + 20x + 3x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-7 + 20x + 3x2 = 0 + 2x2 + -2x2
-7 + 20x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + 20x + 3x2 = 0

Factor a trinomial.
(-7 + -1x)(1 + -3x) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-7, 0.3333333333}

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