7x(x+5)=6x+30

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Solution for 7x(x+5)=6x+30 equation:


Simplifying
7x(x + 5) = 6x + 30

Reorder the terms:
7x(5 + x) = 6x + 30
(5 * 7x + x * 7x) = 6x + 30
(35x + 7x2) = 6x + 30

Reorder the terms:
35x + 7x2 = 30 + 6x

Solving
35x + 7x2 = 30 + 6x

Solving for variable 'x'.

Reorder the terms:
-30 + 35x + -6x + 7x2 = 30 + 6x + -30 + -6x

Combine like terms: 35x + -6x = 29x
-30 + 29x + 7x2 = 30 + 6x + -30 + -6x

Reorder the terms:
-30 + 29x + 7x2 = 30 + -30 + 6x + -6x

Combine like terms: 30 + -30 = 0
-30 + 29x + 7x2 = 0 + 6x + -6x
-30 + 29x + 7x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-30 + 29x + 7x2 = 0

Factor a trinomial.
(-5 + -1x)(6 + -7x) = 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 '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Divide each side by '-7'. x = 0.8571428571 Simplifying x = 0.8571428571

Solution

x = {-5, 0.8571428571}

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