4x^2-31x+42=-6x+6

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Solution for 4x^2-31x+42=-6x+6 equation:


Simplifying
4x2 + -31x + 42 = -6x + 6

Reorder the terms:
42 + -31x + 4x2 = -6x + 6

Reorder the terms:
42 + -31x + 4x2 = 6 + -6x

Solving
42 + -31x + 4x2 = 6 + -6x

Solving for variable 'x'.

Reorder the terms:
42 + -6 + -31x + 6x + 4x2 = 6 + -6x + -6 + 6x

Combine like terms: 42 + -6 = 36
36 + -31x + 6x + 4x2 = 6 + -6x + -6 + 6x

Combine like terms: -31x + 6x = -25x
36 + -25x + 4x2 = 6 + -6x + -6 + 6x

Reorder the terms:
36 + -25x + 4x2 = 6 + -6 + -6x + 6x

Combine like terms: 6 + -6 = 0
36 + -25x + 4x2 = 0 + -6x + 6x
36 + -25x + 4x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
36 + -25x + 4x2 = 0

Factor a trinomial.
(9 + -4x)(4 + -1x) = 0

Subproblem 1

Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25

Subproblem 2

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

Solution

x = {2.25, 4}

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