(x-5)(x-6)=-15x+62

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Solution for (x-5)(x-6)=-15x+62 equation: 


Simplifying
(x + -5)(x + -6) = -15x + 62

Reorder the terms:
(-5 + x)(x + -6) = -15x + 62

Reorder the terms:
(-5 + x)(-6 + x) = -15x + 62

Multiply (-5 + x) * (-6 + x)
(-5(-6 + x) + x(-6 + x)) = -15x + 62
((-6 * -5 + x * -5) + x(-6 + x)) = -15x + 62
((30 + -5x) + x(-6 + x)) = -15x + 62
(30 + -5x + (-6 * x + x * x)) = -15x + 62
(30 + -5x + (-6x + x2)) = -15x + 62

Combine like terms: -5x + -6x = -11x
(30 + -11x + x2) = -15x + 62

Reorder the terms:
30 + -11x + x2 = 62 + -15x

Solving
30 + -11x + x2 = 62 + -15x

Solving for variable 'x'.

Reorder the terms:
30 + -62 + -11x + 15x + x2 = 62 + -15x + -62 + 15x

Combine like terms: 30 + -62 = -32
-32 + -11x + 15x + x2 = 62 + -15x + -62 + 15x

Combine like terms: -11x + 15x = 4x
-32 + 4x + x2 = 62 + -15x + -62 + 15x

Reorder the terms:
-32 + 4x + x2 = 62 + -62 + -15x + 15x

Combine like terms: 62 + -62 = 0
-32 + 4x + x2 = 0 + -15x + 15x
-32 + 4x + x2 = -15x + 15x

Combine like terms: -15x + 15x = 0
-32 + 4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 4}

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