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

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


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

Reorder the terms:
x(-3 + 5x) = -4(x + -1)
(-3 * x + 5x * x) = -4(x + -1)
(-3x + 5x2) = -4(x + -1)

Reorder the terms:
-3x + 5x2 = -4(-1 + x)
-3x + 5x2 = (-1 * -4 + x * -4)
-3x + 5x2 = (4 + -4x)

Solving
-3x + 5x2 = 4 + -4x

Solving for variable 'x'.

Reorder the terms:
-4 + -3x + 4x + 5x2 = 4 + -4x + -4 + 4x

Combine like terms: -3x + 4x = 1x
-4 + 1x + 5x2 = 4 + -4x + -4 + 4x

Reorder the terms:
-4 + 1x + 5x2 = 4 + -4 + -4x + 4x

Combine like terms: 4 + -4 = 0
-4 + 1x + 5x2 = 0 + -4x + 4x
-4 + 1x + 5x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-4 + 1x + 5x2 = 0

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


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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-1, 0.8}

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