x(5x-1)=7x-3

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Solution for x(5x-1)=7x-3 equation:


Simplifying
x(5x + -1) = 7x + -3

Reorder the terms:
x(-1 + 5x) = 7x + -3
(-1 * x + 5x * x) = 7x + -3
(-1x + 5x2) = 7x + -3

Reorder the terms:
-1x + 5x2 = -3 + 7x

Solving
-1x + 5x2 = -3 + 7x

Solving for variable 'x'.

Reorder the terms:
3 + -1x + -7x + 5x2 = -3 + 7x + 3 + -7x

Combine like terms: -1x + -7x = -8x
3 + -8x + 5x2 = -3 + 7x + 3 + -7x

Reorder the terms:
3 + -8x + 5x2 = -3 + 3 + 7x + -7x

Combine like terms: -3 + 3 = 0
3 + -8x + 5x2 = 0 + 7x + -7x
3 + -8x + 5x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
3 + -8x + 5x2 = 0

Factor a trinomial.
(3 + -5x)(1 + -1x) = 0

Subproblem 1

Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6

Subproblem 2

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

Solution

x = {0.6, 1}

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