x(5x+4)=2x^2-7x+4

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Solution for x(5x+4)=2x^2-7x+4 equation: 


Simplifying
x(5x + 4) = 2x2 + -7x + 4

Reorder the terms:
x(4 + 5x) = 2x2 + -7x + 4
(4 * x + 5x * x) = 2x2 + -7x + 4
(4x + 5x2) = 2x2 + -7x + 4

Reorder the terms:
4x + 5x2 = 4 + -7x + 2x2

Solving
4x + 5x2 = 4 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + 4x + 7x + 5x2 + -2x2 = 4 + -7x + 2x2 + -4 + 7x + -2x2

Combine like terms: 4x + 7x = 11x
-4 + 11x + 5x2 + -2x2 = 4 + -7x + 2x2 + -4 + 7x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-4 + 11x + 3x2 = 4 + -7x + 2x2 + -4 + 7x + -2x2

Reorder the terms:
-4 + 11x + 3x2 = 4 + -4 + -7x + 7x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-4 + 11x + 3x2 = 0 + -7x + 7x + 2x2 + -2x2
-4 + 11x + 3x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
-4 + 11x + 3x2 = 0 + 2x2 + -2x2
-4 + 11x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 11x + 3x2 = 0

Factor a trinomial.
(-4 + -1x)(1 + -3x) = 0


Subproblem 1
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

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 = {-4, 0.3333333333}

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