5(3x-7)+x(3x-7)=0

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Solution for 5(3x-7)+x(3x-7)=0 equation:


Simplifying
5(3x + -7) + x(3x + -7) = 0

Reorder the terms:
5(-7 + 3x) + x(3x + -7) = 0
(-7 * 5 + 3x * 5) + x(3x + -7) = 0
(-35 + 15x) + x(3x + -7) = 0

Reorder the terms:
-35 + 15x + x(-7 + 3x) = 0
-35 + 15x + (-7 * x + 3x * x) = 0
-35 + 15x + (-7x + 3x2) = 0

Combine like terms: 15x + -7x = 8x
-35 + 8x + 3x2 = 0

Solving
-35 + 8x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(7 + -3x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333

Solution

x = {-5, 2.333333333}

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