(2x-1)(5x+4)=-3x

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Solution for (2x-1)(5x+4)=-3x equation: 


Simplifying
(2x + -1)(5x + 4) = -3x

Reorder the terms:
(-1 + 2x)(5x + 4) = -3x

Reorder the terms:
(-1 + 2x)(4 + 5x) = -3x

Multiply (-1 + 2x) * (4 + 5x)
(-1(4 + 5x) + 2x * (4 + 5x)) = -3x
((4 * -1 + 5x * -1) + 2x * (4 + 5x)) = -3x
((-4 + -5x) + 2x * (4 + 5x)) = -3x
(-4 + -5x + (4 * 2x + 5x * 2x)) = -3x
(-4 + -5x + (8x + 10x2)) = -3x

Combine like terms: -5x + 8x = 3x
(-4 + 3x + 10x2) = -3x

Solving
-4 + 3x + 10x2 = -3x

Solving for variable 'x'.

Reorder the terms:
-4 + 3x + 3x + 10x2 = -3x + 3x

Combine like terms: 3x + 3x = 6x
-4 + 6x + 10x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-4 + 6x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3x + 5x2) = 0

Factor a trinomial.
2((-1 + -1x)(2 + -5x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-1, 0.4}

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